green chaddi

Question 1

Two vectors lying in the xy plane are given by the equations A = 5i+2j and B=2i-3j . The value of A*B is
a. 19k
b. −11k
c. −19k
d. 11k
e. 10i-j

Answer 1

c. −19k

Question 2

Two vectors lying in the xz plane are given by the equations A=2i+3k and B=-i+2k . The value of A*B is
a. j
b. -j
c. 7k
d.−7j
e. i+5j

Answer 2

d. −7j

Question 3

. A particle located at the position vector r = (i+j) m has a force F = (2i+3j) N acting on it. The torque about the origin is
a. (1k )N⋅m
b. (5k )N⋅m
c. (−1k )N⋅m
d. (−5k )N⋅m
e. (2i + 3j )N⋅m

Answer 3

a. (1k )N⋅m

Question 4

A car of mass 1 000 kg moves with a speed of 50 m/s on a circular track of radius 100 m. What is the magnitude of its angular momentum (in kg⋅m2/s) relative to the center of the race track?
a. 5.0 × 10^2
b. 5.0 × 10^6
c. 2.5 × 10^4
d. 2.5 × 10^6
e. 5.0 × 10^3

Answer 4

b. 5.0 × 10^6

Question 5

A solid cylinder of radius R = 1.0 m and mass 10 kg rotates about its axis. When its angular velocity is 10 rad/s, its angular momentum (in kg⋅m2/s) is
a. 50
b. 20.
c. 40.
d. 25.
e. 70.

Answer 5

a. 50.

Question 6

A particle whose mass is 2 kg moves in the xy plane with a constant speed of 3 m/s in the x direction along the line y = 5. What is its angular momentum (in kg⋅m2/s) relative to the origin?
a. −30k
b. 30k
c. −15k
d. 15k
e. 45k

Answer 6

a. −30k

Question 7

A particle whose mass is 2 kg moves in the xy plane with a constant speed of 3 m/s along the direction r = i+j . What is its angular momentum (in kg⋅m2/s) relative to the origin?
a. 0k
b. 6sqrt2k
c. -6sqrt2k
d. 6k
e. −6k

Answer 7

a. 0k

Question 8

A particle whose mass is 2.0 kg moves in the xy plane with a constant speed of 3.0 m/s along the direction r = i+j . What is its angular momentum (in kg⋅m2/s) relative to the point (0, 5.0) meters?
a. 12k
b. 11k
c. 13k
d. 14k
e. 21k

Answer 8

e. 21k

Question 9

In the figure, a 1.6-kg weight swings in a vertical circle at the end of a string having negligible weight. The string is 2 m long. If the weight is released with zero initial velocity from a horizontal position, its angular momentum (in kg⋅m2/s) at the lowest point of its path relative to the center of the circle is approximately

a. 40
b. 10
c. 30
d. 20
e. 50

Answer 9

d. 20

Question 10

A massless rope is wrapped around a uniform cylinder that has radius R and mass M, as shown in the figure. Initially, the unwrapped portion of the rope is vertical and the cylinder is horizontal. The linear acceleration of the cylinder is
a. (2/3)g
b. (1/2)g
c. (1/3)g
d. (1/6)g
e. (5/6)g

Answer 10

a. (2/3)g

Question 11

Two blocks, m1 = 1.0 kg and m2 = 2.0 kg, are connected by a light string as shown in the figure. If the radius of the pulley is 1.0 m and its moment of inertia is 5.0 kg⋅m2, the acceleration of the system is
a. (1/6)g
b. (3/8)g
c. (1/8)g
d. (1/2)g
e. (5/8)g

Answer 11

c. (1/8)g

Question 12

A puck on a frictionless air hockey table has a mass of 5.0 kg and is attached to a cord passing through a hole in the surface as in the figure. The puck is revolving at a distance 2.0 m from the hole with an angular velocity of 3.0 rad/s. The angular momentum of the puck (in kg⋅m2/s) is
a. 80
b. 20
c. 30
d. 60
e. 50

Answer 12

d. 60

Question 13

A pendulum bob of mass m is set into motion in a circular path in a horizontal plane as shown in the figure. The square of the angular momentum of the bob about the vertical axis through the point P is
a. m2 gl3 sin4 θ/cos θ
b. m2 gl3 sin3 θ/cos θ
c. m2 gl3 sin2 θ/cos θ
d. m2 gl3 sin θ/cos θ
e. m2 gl3 sin2 θ

Answer 13

a. m2 gl3 sin4 θ/cos θ

Question 14

A puck on a frictionless air hockey table has a mass of 5.0 g and is attached to a cord passing through a hole in the surface as in the figure. The puck is revolving at a distance 2.0 m from the hole with an angular velocity of 3.0 rad/s. The cord is then pulled from below, shortening the radius to 1.0 m. The new angular velocity (in rad/s) is a. 4.0
b. 6.0
c. 12
d. 2.0
e. 8.0

Answer 14

c. 12

Question 15

A thin rod of mass M and length L is struck at one end by a ball of clay of mass m, moving with speed v as shown in the figure. The ball sticks to the rod. After the collision, the angular momentum of the clay-rod system about A, the midpoint of the rod, is
a. (m + M/3)(vL/2)
b. (m + M/12)(vL/2)
c. (m + M/6)(vL/2)
d. mvL/2
e. mvL

Answer 15

d. mvL/2

Question 16

A particle of mass m = 0.10 kg and speed v0 = 5.0 m/s collides and sticks to the end of a uniform solid cylinder of mass M = 1.0 kg and radius R = 20 cm. If the cylinder is initially at rest and is pivoted about a frictionless axle through its center, what is the final angular velocity (in rad/s) of the system after the collision?
a. 8.1
b. 2.0
c. 6.1
d. 4.2
e. 10

Answer 16

d. 4.2

Question 17

A skater extends her arms horizontally, holding a 5-kg mass in each hand. She is rotating about a vertical axis with an angular velocity of one revolution per second. If she drops her hands to her sides, what will the final angular velocity (in rev/s) be if her moment of inertia remains approximately constant at 5 kg⋅m2, and the distance of the masses from the axis changes from 1 m to 0.1 m?
a. 6
b. 3
c. 9
d. 4
e. 7

Answer 17

b. 3

Question 18

A merry-go-round of radius R = 2.0 m has a moment of inertia I = 250 kg⋅m2, and is rotating at 10 rpm. A child whose mass is 25 kg jumps onto the edge of the merry-go-round, heading directly toward the center at 6.0 m/s. The new angular speed (in rpm) of the merry-go-round is approximately
a. 10
b. 9.2
c. 8.5
d. 7.1
e. 6.4

Answer 18

d. 7.1

Question 19

A solid sphere (radius R, mass M) rolls without slipping down an incline as shown in the figure. The linear acceleration of its center of mass is
a. (5/7)g sin θ
b. (3/5)g sin θ
c. (2/3)g sin θ
d. (1/2)g sin θ
e. (4/5)g sin θ

Answer 19

a. (5/7)g sin θ

Question 20

A solid cylinder rolls without slipping down an incline as shown in the figure. The linear acceleration of its center of mass is
a. (5/7)g sin θ
b. (1/2)g sin θ
c. (2/3)g sin θ
d. (3/5)g sin θ
e. (4/5)g sin θ

Answer 20

c. (2/3)g sin θ

Question 21

A cylindrical shell rolls without slipping down an incline as shown in the figure. The linear acceleration of its center of mass is
a. (5/7)g sin θ
b. (1/2)g sin θ
c. (3/5)g sin θ
d. (2/3)g sin θ
e. (4/5)g sin θ

Answer 21

b. (1/2)g sin θ

Question 22

A solid sphere, spherical shell, solid cylinder and a cylindrical shell all have the same mass m and radius R. If they are all released from rest at the same elevation and roll without slipping, which reaches the bottom of an inclined plane first?
a. solid sphere
b. spherical shell
c. solid cylinder
d. cylindrical shell
e. all take the same time

Answer 22

a. solid sphere

Question 23

Stars originate as large bodies of slowly rotating gas. Because of gravity, these clumps of gas slowly decrease in size. The angular velocity of a star increases as it shrinks because of
a. conservation of angular momentum
b. conservation of linear momentum
c. conservation of energy
d. the law of universal gravitation
e. conservation of mass

Answer 23

a. conservation of angular momentum

Question 24

Five objects of mass m move at velocity at a distance r from an axis of rotation perpendicular to the page through point A, as shown below. The one that has zero angular momentum about that axis is

Answer 24

d. A* vector v pointing to the corner

Question 25

The object shown below has mass m and velocity v . The direction of its angular momentum vector with respect to an axis perpendicular to the page through point O is
a. downwards.
b. to the right.
c. into the page.
d. up out of the page.
e. counterclockwise.

Answer 25

c. into the page.

Question 26

Two objects of mass m1 = 2m and m2 = m move around a rotation axis A in parallel circles of radii r1 = r and r2 = 2r with equal tangential speeds. As they rotate, forces of equal magnitude are applied opposite to their velocities to stop them. Which statement is correct?

a. m2 will stop first because it has the larger initial angular velocity. b. m1 will stop first because it has the smaller radius.
c. m2 will stop first because the torque on it is greater.
d. m1 will stop first because it has the smaller moment of inertia.
e. Both objects will stop at the same time because the angular accelerations are equal.

Answer 26

c. m2 will stop first because the torque on it is greater.

Question 27

A torque can be exerted on a body with a fixed axis of rotation
a. only by a centripetal force.
b. only by a force directed radially outwards.
c. only by a tangential force.
d. only by a force with a component directed radially outwards.
e. by any force not pointing directly toward or away from the axis of rotation.

Answer 27

e. by any force not pointing directly toward or away from the axis of rotation.

Question 28

Five identical cylinders are each acted on by forces of equal magnitude. Which force exerts the biggest torque about the central axes of the cylinders?

Answer 28

a. cylinder with F pointing STRAIGHT to the right

Question 29

The diagram below shows five cylinders, each cylinder rotating with constant angular velocity about its central axis. The magnitude of the tangential speed of one point of each cylinder is shown, along with each cylinder’s radius and mass. Which cylinder has the largest angular momentum?

Answer 29

v = 4 m/sr = 2 m M = 20 kg

Question 30

The diagram below shows five thin cylindrical shells, each shell rotating with constant angular velocity about its central axis. The magnitude of the tangential speed of one point of each cylinder is shown, along with each cylinder’s radius and mass. Which cylindrical shell has the largest angular momentum?

Answer 30

v = 4 m/sr = 2 m M = 20 kg

Question 31

The diagram below shows five 20-kg rods of the same 2.0-m length free to rotate about axes through the rods, as indicated. Which rod experiences the greatest magnitude gravitational torque?

Answer 31

Ruler with dot on 2.0

Question 32

A force is applied to a cylindrical roll of paper of radius R and mass M by pulling on the paper as shown. The acceleration of the center of mass of the roll of paper (when it rolls without slipping) is
a. 1/2 F/M
b. F/M
c. 3/2 F/M
d. 4/3 F/M
e. 2F/M

Answer 32

d. 4/3 F/M

Question 33

A 0.5 kg fish, hooked as shown below, starts to swim away at a speed of 3 m/s. The angular momentum of the fish relative to the hand holding the fishing rod is about
a. 3 kgm^2/s
b. 6 kgm^2/s
c. 17 kgm^2/s
d. 30 kgm^2/s
e. 60 kgm^2/s

Answer 33

a. 3 kgm^2/s

Question 34

Exhibit 11-1Two blocks of masses m1 and m2 are connected by a light cord that passes over a pulley of mass M, as shown. Block m2 slides on a frictionless horizontal surface. The blocks and pulley are initially at rest. When m1 is released, the blocks accelerate and the pulley rotates. The total angular momentum of the system of the two blocks and the pulley relative to the axis of rotation of the pulley is Use this exhibit to answer the following question(s). Refer to Exhibit 11-1. The total angular momentum of the system of the two blocks and the pulley relative to the axis of rotation of the pulley is
a. the same at all times.
b. proportional to l1, the length of string from the pulley to m1.
c. proportional to l2, the length of string from the pulley to m2.
d. conserved because the Earth doesn’t move.
e. proportional to the speed of the blocks.

Answer 34

e. proportional to the speed of the blocks.

Question 35

. Refer to Exhibit 11-1. The total angular momentum of the system of the two blocks and the pulley relative to the axis of rotation of the pulley is
a. proportional to the radius of the pulley.
b. proportional to the speed of the blocks.
c. proportional to the length of the string.
d. to all of the above.
e. only to (a) and (b) above.

Answer 35

b. proportional to the speed of the blocks.

Question 36

When an object is effectively isolated from external torques, like an ice skater twirling on the tip of one skate, the angular momentum of the object
a. can be increased by shifting mass out away from the axis of rotation.
b. can be decreased by shifting mass out away from the axis of rotation.
c. can be increased by shifting mass in toward the axis of rotation. d. can be decreased by shifting mass in toward the axis of rotation. e. cannot be changed except by friction at the point of contact.

Answer 36

e. cannot be changed except by friction at the point of contact.

Question 37

A hockey puck traveling at speed v on essentially frictionless ice collides elastically with one end of a straight stick lying flat on the ice. In this collision
a. momentum is conserved.
b. angular momentum is conserved.
c. energy is conserved.
d. all of the above are conserved.
e. only momentum and angular momentum are conserved.

Answer 37

d. all of the above are conserved.

Question 38

A hockey puck traveling at speed v on essentially frictionless ice collides with one end of a straight stick lying flat on the ice and sticks to that end. In this collision
a. momentum is conserved.
b. angular momentum is conserved.
c. energy is conserved.
d. all of the above are conserved.
e. only momentum and angular momentum are conserved.

Answer 38

e. only momentum and angular momentum are conserved.

Question 39

A space station out beyond the solar system is rotating with constant angular velocity. A spaceship heading into the station along a diameter of the station, uses its rockets to brake, and then docks inside the station at its center. When the spaceship docks, the angular momentum of the system consisting of the station and ship a. is less than the original angular momentum of the station.
b. is the same as the original angular momentum of the station.
c. is greater than the original angular momentum of the station.
d. is less than the original angular momentum of the station, but the angular velocity increases.
e. is greater than the original angular momentum of the station, but the angular velocity decreases.

Answer 39

b. is the same as the original angular momentum of the station.

Question 40

A top is set spinning so that the rotation is counterclockwise around its axis when viewed from above. When the top is placed on a level surface it happens that its axis of rotation is not quite vertical. Viewed from above, which way does the rotational axis of the top precess?
a. clockwise
b. counterclockwise
c. It’s random, if it starts clockwise it will continue clockwise, and vice versa, i.e., a 50% chance either way.
d. The direction depends on the little shove given to the axis when the top is placed on the surface.
e. In the northern hemisphere it will be clockwise, in the southern hemisphere it will be counterclockwise.

Answer 40

b. counterclockwise

Question 41

A 3.0-kg particle has a position vector given by r = (2.0t^2i + 3.0j) where r is in meters and t is in seconds. What is the angular momentum of the particle, in kg⋅m2/s, about the origin at t = 2 s?
a. 72k
b. −72k
c. 24k
d. −24k
e. 22k

Answer 41

b. −72k

Question 42

If L represents angular momentum, I represents moment of inertia, p represents linear momentum, m represents mass, and r represents a distance, which of the following can represent kinetic energy?
a. p2/2m
b. L2/2I
c. rpI
d. all of the above
e. both (a) and (b)

Answer 42

e. both (a) and (b)

Question 43

Halley’s comet moves about the sun in an elliptical orbit with its closest approach to the sun being 0.59 A.U. and its furthest distance being 35 A.U. [1 Astronomical Unit (A.U.) is the Earth-sun distance.] If the comet’s speed at closest approach is 54 km/s, what is its speed when it is farthest from the sun?

Answer 43

910 m/s

Question 44

What is the angular momentum of the moon about the Earth? The mass of the moon is 7.35 × 1022 kg, the center-to-center separation of the Earth and the moon is 3.84 × 105 km, and the orbital period of the moon is 27.3 days. Ignore the small offset of the center of mass of the system from the center of the Earth in your calculation.

Answer 44

2.89 * 10^34 kgm^2/s

Question 45

A regulation basketball has a 25.0-cm diameter and a mass of 0.560 kg. It may be approximated as a thin spherical shell with a moment of inertia MR2. Starting from rest, how long will it take a basketball to roll without slipping 4.00 m down an incline at 30.0° to the horizontal?

Answer 45

1.65 s

Question 46

A coin with a diameter 3.00 cm rolls up a 30.0° inclined plane. The coin starts out with an initial angular speed of 60.0 rad/s and rolls in a straight line without slipping. If the moment of inertia of the coin is MR2, how far will the coin roll up the inclined plane?

Answer 46

12.4 cm

Question 47

A body of mass 5.0 kg is suspended by a spring which stretches 10 cm when the mass is attached. It is then displaced downward an additional 5.0 cm and released. Its position as a function of time is approximately
a. y = −0.10 sin 9.9t
b. y = 0.10 cos 9.9t
c. y = −0.10 cos (9.9t + .1)
d. y = 0.10 sin (9.9t + 5)
e. y = −0.05 cos 9.9t

Answer 47

e. y = −0.05 cos 9.9t

Question 48

A body oscillates with simple harmonic motion along the x axis. Its displacement varies with time according to the equation x = 5.0 cos (πt). The magnitude of the acceleration (in m/s2) of the body at t = 1.0 s is approximately
a. 3.5
b. 49
c. 14
d. 43
e. 4.3

Answer 48

b. 49

Question 49

A body oscillates with simple harmonic motion along the x axis. Its displacement varies with time according to the equation x = 5 sin (πt + π/3). The phase (in rad) of the motion at t = 2 s is
a. 7π/3
b. π/3
c. π
d. 5π/3
e. 2π

Answer 49

a. 7π/3

Question 50

A body oscillates with simple harmonic motion along the x axis. Its displacement varies with time according to the equation x = 5.0 sin (πt + π/3). The velocity (in m/s) of the body at t = 1.0 s is
a. +7.9
b. −7.9
c. −14
d. +14
e. −5.0

Answer 50

b. −7.9

Question 51

The motion of a particle connected to a spring is described by x = 10 sin (πt). At what time (in s) is the potential energy equal to the kinetic energy?
a. 0
b. 0.25
c. 0.50
d. 0.79
e. 1.0

Answer 51

b. 0.25

Question 52

The amplitude of a system moving with simple harmonic motion is doubled. The total energy will then be
a. 4 times as large
b. 3 times as large
c. 2 times as large
d. the same as it was
e. half as much

Answer 52

a. 4 times as large

Question 53

A mass m = 2.0 kg is attached to a spring having a force constant k = 290 N/m as in the figure. The mass is displaced from its equilibrium position and released. Its frequency of oscillation (in Hz) is approximately

a. 12
b. 0.50
c. 0.010
d. 1.9
e. 0.080

Answer 53

d. 1.9

Question 54

The mass in the figure slides on a frictionless surface. If m = 2 kg, k1 = 800 N/m and k2 = 500 N/m, the frequency of oscillation (in Hz) is approximately

a. 6
b. 2
c. 4
d. 8
e. 10

Answer 54

c. 4

Question 55

Two circus clowns (each having a mass of 50 kg) swing on two flying trapezes (negligible mass, length 25 m) shown in the figure. At the peak of the swing, one grabs the other, and the two swing back to one platform. The time for the forward and return motion is

a. 10 s
b. 50 s
c. 15 s
d. 20 s
e. 25 s

Answer 55

a. 10 s

Question 56

A uniform rod (mass m = 1.0 kg and length L = 2.0 m) pivoted at one end oscillates in a vertical plane as shown below. The period of oscillation (in s) is approximately

a. 4.0
b. 1.6
c. 3.2
d. 2.3
e. 2.0

Answer 56

d. 2.3

Question 57

A horizontal plank (m = 2.0 kg, L = 1.0 m) is pivoted at one end. A spring (k = 1.0 × 103 N/m) is attached at the other end, as shown in the figure. Find the angular frequency (in rad/s) for small oscillations.

a. 39
b. 44
c. 55
d. 66
e. 25

Answer 57

a. 39

Question 58

The figure shows a uniform rod (length L = 1.0 m, mass = 2.0 kg) suspended from a pivot a distance d = 0.25 m above its center of mass. The angular frequency (in rad/s) for small oscillations is approximately

a. 1.0
b. 2.5
c. 1.5
d. 4.1
e. 3.5

Answer 58

d. 4.1

Question 59

In the figure below, a disk (radius R = 1.0 m, mass = 2.0 kg) is suspended from a pivot a distance d = 0.25 m above its center of mass. For a circular disk, . The angular frequency (in rad/s) for small oscillations is approximately

a. 4.2
b. 2.1
c. 1.5
d. 1.0
e. 3.8

Answer 59

b. 2.1

Question 60

In the figure below, a hoop (radius R = 1.0 m, mass = 2.0 kg) having four spokes of negligible mass is suspended from a pivot a distance d = .25 m above its center of mass. The angular frequency (in rad/s) for small oscillations is approximately

a. 4.0
b. 2.5
c. 1.5
d. 1.0
e. 0.5

Answer 60

c. 1.5

Question 61

A torsional pendulum consists of a solid disk (mass = 2.0 kg, radius = 1.0 m) suspended by a wire attached to a rigid support. The body oscillates about the support wire. If the torsion constant is 16 N⋅m/rad. What is the angular frequency (in rad/s)?

a. 2
b. 4
c. 6
d. 8
e. 7

Answer 61

b. 4

Question 62

The mass in the figure below slides on a frictionless surface. When the mass is pulled out, spring 1 is stretched a distance x1 from its equilibrium position and spring 2 is stretched a distance x2. The spring constants are k1 and k2 respectively. The force pulling back on the mass is:

a. −k2x1.
b. −k2x2.
c. −(k1x1 + k2x2).
d. -k1+k2/2 (x1+x2)
e. -k1+k2/k1k2(x1+x2)

Answer 62

b. −k2x2.

Question 63

A hoop, a solid cylinder, and a solid sphere all have the same mass m and the same radius R. Each is mounted to oscillate about an axis a distance 0.5 R from the center. The axis is perpendicular to the circular plane of the hoop and the cylinder and to an equatorial plane of the sphere as shown below. Which is the correct ranking in order of increasing angular frequency ω?

a. hoop, cylinder, sphere
b. cylinder, sphere, hoop
c. sphere, cylinder, hoop
d. hoop, sphere, cylinder
e. sphere, hoop, cylinder

Answer 63

a. hoop, cylinder, sphere

Question 64

Three pendulums with strings of the same length and bobs of the same mass are pulled out to angles θ1, θ2 and θ3 respectively and released. The approximation sin θ = θ holds for all three angles, with θ3 > θ2 > θ1. How do the angular frequencies of the three pendulums compare?
a. ω3 > ω2 > ω1
b. Need to know amplitudes to answer this question.
c. Need to know sqrt g/L to answer this question.
d. ω1 > ω2 > ω3
e. ω1 = ω2 = ω3

Answer 64

e. ω1 = ω2 = ω3

Question 65

A weight of mass m is at rest at O when suspended from a spring, as shown. When it is pulled down and released, it oscillates between positions A and B. Which statement about the system consisting of the spring and the mass is correct?

a. The gravitational potential energy of the system is greatest at A.
b. The elastic potential energy of the system is greatest at O.
c. The rate of change of momentum has its greatest magnitude at A and B.
d. The rate of change of gravitational potential energy is smallest at O.
e. The rate of change of gravitational potential energy has its greatest magnitude at A and B.

Answer 65

c. The rate of change of momentum has its greatest magnitude at A and B.

Question 66

An object of mass m is attached to string of length L. When it is released from point A, the object oscillates between points A and B. Which statement about the system consisting of the pendulum and the Earth is correct?

a. The gravitational potential energy of the system is greatest at A and B.
b. The kinetic energy of mass m is greatest at point O.
c. The greatest rate of change of momentum occurs at A and B.
d. All of the above are correct.
e. Only (a) and (b) above are correct.

Answer 66

d. All of the above are correct.

Question 67

Refer to Exhibit 15-1. A point or points at which the object has positive velocity and zero acceleration is(are)
a. B
b. C
c. D
d. B and D
e. A and E

Answer 67

e. A and E

Question 68

Refer to Exhibit 15-1. The point at which the object has negative velocity and zero acceleration is
a. A
b. B
c. C
d. D
e. E

Answer 68

c. C

Question 69

. Refer to Exhibit 15-1. The point at which the object has zero velocity and positive acceleration is
a. A
b. B
c. C
d. D
e. E

Answer 69

d. D

Question 70

Refer to Exhibit 15-1. The point at which the object has zero velocity and negative acceleration is
a. A
b. B
c. C
d. D
e. E

Answer 70

b. B

Question 71

In an inertia balance, a body supported against gravity executes simple harmonic oscillations in a horizontal plane under the action of a set of springs. If a 1.00 kg body vibrates at 1.00 Hz, a 2.00 kg body will vibrate at
a. 0.500 Hz.
b. 0.707 Hz.
c. 1.00 Hz.
d. 1.41 Hz.
e. 2.00 Hz.

Answer 71

b. 0.707 Hz.

Question 72

At sea level, at a latitude where , a pendulum that takes 2.00 s for a complete swing back and forth has a length of 0.993 m. What is the value of g in m/s2 at a location where the length of such a pendulum is 0.970 m?
a. 0.098 3
b. 3.05
c. 9.57
d. 10.0
e. 38.3

Answer 72

c. 9.57

Question 73

Suppose it were possible to drill a frictionless cylindrical channel along a diameter of the Earth from one side of the Earth to another. A body dropped into such a channel will only feel the gravitational pull of mass within a sphere of radius equal to the distance of the mass from the center of the Earth. The density of the Earth is 5.52 × 103 kg/m3 and G = 6.67 × 10−11 N⋅m2/kg2. The mass will oscillate with a period of
a. 84.4 min.
b. 169 min.
c. 24.0 h.
d. 1 130 h.
e. 27.2 d.

Answer 73

a. 84.4 min.

Question 74

A 2.00 m-long 6.00 kg ladder pivoted at the top hangs down from a platform at the circus. A 42.0 kg trapeze artist climbs to a point where her center of mass is at the center of the ladder and swings at the system’s natural frequency. The angular frequency (in s−1) of the system of ladder and woman is
a. 1.01.
b. 3.07.
c. 4.03.
d. 8.05.
e. 16.2.

Answer 74

b. 3.07.

Question 75

Ellen says that whenever the acceleration is directly proportional to the displacement of an object from its equilibrium position, the motion of the object is simple harmonic motion. Mary says this is true only if the acceleration is opposite in direction to the displacement. Which one, if either, is correct?
a. Ellen, because ω2 is directly proportional to the constant multiplying the displacement and to the mass.
b. Ellen, because ω2 is directly proportional to the mass.
c. Mary, because ω2 is directly proportional to the constant multiplying the displacement and to the mass.
d. Mary, because ω2 is directly proportional to the mass.
e. Mary, because the second derivative of an oscillatory function like sin(ωt) or cos(ωt) is always proportional to the negative of the original function.

Answer 75

e. Mary, because the second derivative of an oscillatory function like sin(ωt) or cos(ωt) is always proportional to the negative of the original function.

Question 76

John says that the value of the function cos[ω(t + T) + ϕ], obtained one period T after time t, is greater than cos(ωt + ϕ) by 2π. Larry says that it is greater by the addition of 1.00 to cos(ωt + ϕ). Which one, if either, is correct?
a. John, because ωT = 2π.
b. John, because ωT = 1 radian.
c. Larry, because ωT = 2π.
d. Larry, because ωT = 1 radian.
e. Neither, because cos(θ + 2π) = cosθ.

Answer 76

e. Neither, because cos(θ + 2π) = cosθ.

Question 77

. Simple harmonic oscillations can be modeled by the projection of circular motion at constant angular velocity onto a diameter of the circle. When this is done, the analog along the diameter of the acceleration of the particle executing simple harmonic motion is
a. the displacement from the center of the diameter of the projection of the position of the particle on the circle.
b. the projection along the diameter of the velocity of the particle on the circle.
c. the projection along the diameter of tangential acceleration of the particle on the circle.
d. the projection along the diameter of centripetal acceleration of the particle on the circle.
e. meaningful only when the particle moving in the circle also has a non-zero tangential acceleration.

Answer 77

d. the projection along the diameter of centripetal acceleration of the particle on the circle.

Question 78

When a damping force is applied to a simple harmonic oscillator which has angular frequency ω0 in the absence of damping, the new angular frequency ω is such that
a. ω < ω0.
b. ω = ω0.
c. ω > ω0.
d. ωT < ω0T0.
e. ωT > ω0T0.

Answer 78

a. ω < ω0.

Question 79

When a damping force is applied to a simple harmonic oscillator which has period T0 in the absence of damping, the new period T is such that
a. T < T0.
b. T = T0.
c. T > T0.
d. ωT < ω0T0.
e. ωT > ω0T0.

Answer 79

c. T > T0.

Question 80

. To double the total energy of a mass oscillating at the end of a spring with amplitude A, we need to
a. increase the angular frequency by sqrt2.
b. increase the amplitude by sqrt2.
c. increase the amplitude by 2.
d. increase the angular frequency by 2.
e. increase the amplitude by 4 and decrease the angular frequency by 1/sqrt2.

Answer 80

b. increase the amplitude by sqrt2.

Question 81

A damped oscillator is released from rest with an initial displacement of 10.00 cm. At the end of the first complete oscillation the displacement reaches 9.05 cm. When 4 more oscillations are completed, what is the displacement reached?
a. 7.41 cm
b. 6.71 cm
c. 6.07 cm
d. 5.49 cm
e. 5.25 cm

Answer 81

c. 6.07 cm

Question 82

The oscillation of the 2.0-kg mass on a spring is described by where x is in centimeters and t is in seconds. What is the force constant of the spring?
a. 4.0 N/m
b. 0.80 N/m
c. 16 N/m
d. 32 N/m
e. 2.0 N/m

Answer 82

d. 32 N/m

Question 83

Which of the following combinations of variables results in the greatest period for a pendulum?
a. length = L, mass = M, and maximum angular displacement = 3 degrees
b. length = 2L, mass = M/2, and maximum angular displacement = 1 degree
c. length = 1.5L, mass = 2M, and maximum angular displacement = 2 degrees
d. length = sqrt2 L, mass = sqrt2 M, and maximum angular displacement = sqrt degrees
e. length = sqrt3 L, mass = 4M, and maximum angular displacement = 4 degrees

Answer 83

b. length = 2L, mass = M/2, and maximum angular displacement = 1 degree

Question 84

An automobile (m = 1.00 × 103 kg) is driven into a brick wall in a safety test. The bumper behaves like a spring (k = 5.00 × 106 N/m), and is observed to compress a distance of 3.16 cm as the car is brought to rest. What was the initial speed of the automobile?

Answer 84

2.23 m/s

Question 85

The mat of a trampoline is held by 32 springs, each having a spring constant of 5 000 N/m. A person with a mass of 40.0 kg jumps from a platform 1.93 m high onto the trampoline. Determine the stretch of each of the springs.

Answer 85

9.97 cm

Question 86

An archer pulls her bow string back 0.40 m by exerting a force that increases uniformly from zero to 240 N. What is the equivalent spring constant of the bow, and how much work is done in pulling the bow?

Answer 86

600 N/m, 48 J

Question 87

An ore car of mass 4 000 kg starts from rest and rolls downhill on tracks from a mine. A spring with k = 400 000 N/m is located at the end of the tracks. At the spring’s maximum compression, the car is at an elevation 10 m lower than its elevation at the starting point. How much is the spring compressed in stopping the ore car? Ignore friction.

Answer 87

1.4 m

Question 88

The motion of a piston in an auto engine is simple harmonic. If the piston travels back and forth over a distance of 10 cm, and the piston has a mass of 1.5 kg, what is the maximum speed of the piston and the maximum force acting on the piston when the engine is running at 4 200 rpm?

Answer 88

22 m/s, 14500 N

Question 89

The wavelength of light visible to the human eye is on the order of 5 × 10−7 m. If the speed of light in air is 3 × 108 m/s, find the frequency of the lightwave.
a. 3 × 10^7 Hz
b. 4 × 10^9 Hz
c. 5 × 10^11 Hz
d. 6 × 10^14 Hz
e. 4 × 10^15 Hz

Answer 89

d. 6 × 10^14 Hz

Question 90

The speed of a 10-kHz sound wave in seawater is approximately 1 500 m/s. What is its wavelength in sea water?
a. 5.0 cm
b. 10 cm
c. 15 cm
d. 20 cm
e. 29 cm

Answer 90

c. 15 cm

Question 91

Bats can detect small objects such as insects that are of a size on the order of a wavelength. If bats emit a chirp at a frequency of 60 kHz and the speed of soundwaves in air is 330 m/s, what is the smallest size insect they can detect?
a. 1.5 mm
b. 3.5 mm
c. 5.5 mm
d. 7.5 mm
e. 9.8 mm

Answer 91

c. 5.5 mm

Question 92

Ocean waves with a wavelength of 120 m are coming in at a rate of 8 per minute. What is their speed?
a. 8.0 m/s
b. 16 m/s
c. 24 m/s
d. 30 m/s
e. 4.0 m/s

Answer 92

b. 16 m/s

Question 93

An earthquake emits both S-waves and P-waves which travel at different speeds through the Earth. A P-wave travels at 9 000 m/s and an S-wave travels at 5 000 m/s. If P-waves are received at a seismic station 1.00 minute before an S-wave arrives, how far away is the earthquake center?
a. 88.9 km
b. 1 200 km
c. 675 km
d. 240 km
e. 480 km

Answer 93

c. 675 km

Question 94

A piano string of density 0.005 0 kg/m is under a tension of 1 350 N. Find the velocity with which a wave travels on the string.
a. 260 m/s
b. 520 m/s
c. 1 040 m/s
d. 2 080 m/s
e. 4 160 m/s

Answer 94

b. 520 m/s

Question 95

A 100-m long transmission cable is suspended between two towers. If the mass density is 2.01 kg/m and the tension in the cable is 3.00 × 104 N, what is the speed of transverse waves on the cable?
a. 60 m/s
b. 122 m/s
c. 244 m/s
d. 310 m/s
e. 1 500 m/s

Answer 95

b. 122 m/s

Question 96

Transverse waves are traveling on a 1.00-m long piano string at 500 m/s. If the points of zero vibration occur at one-half wavelength (where the string is fastened at both ends), find the frequency of vibration.
a. 250 Hz
b. 500 Hz
c. 1 000 Hz
d. 2 000 Hz
e. 2 500 Hz

Answer 96

a. 250 Hz

Question 97

The lowest A on a piano has a frequency of 27.5 Hz. If the tension in the 2.00-m string is 308 N, and one-half wavelength occupies the string, what is the mass of the wire?
a. 0.025 kg
b. 0.049 kg
c. 0.051 kg
d. 0.081 kg
e. 0.037 kg

Answer 97

c. 0.051 kg

Question 98

If y = 0.02 sin (30x − 400t) (SI units), the frequency of the wave is
a. 30 Hz
b. 15/π Hz
c. 200/π Hz
d. 400 Hz
e. 800π Hz

Answer 98

c. 200/π Hz

Question 99

If y = 0.02 sin (30x − 400t) (SI units), the wavelength of the wave is
a. π/15 m
b. 15/π m
c. 60π m
d. 4.2 m
e. 30 m

Answer 99

a. π/15 m

Question 100

If y = 0.02 sin (30x − 400t) (SI units), the velocity of the wave is
a. 3/40 m/s
b. 40/3 m/s
c. 60π/400 m/s
d. 400/60π m/s
e. 400 m/s

Answer 100

b. 40/3 m/s

Question 101

If y = 0.02 sin (30x − 400t) (SI units), the angular frequency of the wave is
a. 30 rad/s
b. 30/2π rad/s
c. 400/2π rad/s
d. 400 rad/s
e. 40/3 rad/s

Answer 101

d. 400 rad/s

Question 102

If y = 0.02 sin (30x − 400t) (SI units), the wave number is
a. 30 rad/m
b. 30/2π rad/m
c. 400/2π rad/m
d. 400 rad/m
e. 60π rad/m

Answer 102

a. 30 rad/m

Question 103

. If y = 0.02 sin (30x − 400t) (SI units) and if the mass density of the string on which the wave propagates is 0.005 kg/m, then the transmitted power is
a. 1.03 W
b. 2.13 W
c. 4.84 W
d. 5.54 W
e. 106 W

Answer 103

b. 2.13 W

Question 104

Write the equation of a wave, traveling along the +x axis with an amplitude of 0.02 m, a frequency of 440 Hz, and a speed of 330 m/sec.
a. y = 0.02 sin [880π(x/330 − t)]
b. y = 0.02 cos [880π x/330 − 440t]
c. y = 0.02 sin [880π(x/330 + t)]
d. y = 0.02 sin [2π(x/330 + 440t)]
e. y = 0.02 cos [2π(x/330 + 440t)]

Answer 104

a. y = 0.02 sin [880π(x/330 − t)]

Question 105

. For the wave described by y = 0.15sin[pi/16(2x-64t)] (SI Units), determine the first positive x coordinate where y is a maximum when t = 0.
a. 16 m
b. 8 m
c. 4 m
d. 2 m
e. 13 m

Answer 105

c. 4 m

Question 106

For the wave described by y = 0.15 sin [pi/16 (2x-64t)] (SI Units) , determine the x coordinate of the second maximum when t = 0.
a. 20 m
b. 18 m
c. 24 m
d. 28 m
e. 16 m

Answer 106

a. 20 m

Question 107

For the wave described by y = 0.02 sin (kx) at t = 0 s, the first maximum at a positive x coordinate occurs where x = 4 m. Where on the positive x axis does the second maximum occur?
a. 20 m
b. 18 m
c. 24 m
d. 28 m
e. 16 m

Answer 107

a. 20 m

Question 108

For the transverse wave described by y = 0.15 sin[pi/16 (2x-64t)] (SI Units) , determine the maximum transverse speed of the particles of the medium.
a. 0.192 m/s
b. 0.6π m/s
c. 9.6 m/s
d. 4 m/s
e. 2 m/s

Answer 108

b. 0.6π m/s

Question 109

. Which of the following is a solution to the wave equation, alpha^2y/alphax^2 = 1/v^2 alpha^2y/alphat^2 ?
a. e^-x/x sin x
b. (cos kx) (sin ωt)
c. e−x sin ωt
d. e−x sin (kx − ωt)
e. e−x cos t

Answer 109

b. (cos kx) (sin ωt)

Question 110

Find the period of a wave of 100-m wavelength in deep water where sqrt g lamba / 2pi .
a. 5.0 s
b. 8.0 s
c. 12.5 s
d. 15 s
e. 0.125 s

Answer 110

b. 8.0 s

Question 111

A piano wire of length 1.5 m vibrates so that one-half wavelength is contained on the string. If the frequency of vibration is 65 Hz, the amplitude of vibration is 3.0 mm, and the density is 15 g/m, how much energy is transmitted per second down the wire?
a. 21 W
b. 11 W
c. 5.4 W
d. 2.2 W
e. 1.1 W

Answer 111

d. 2.2 W

Question 112

A student attaches a length of nylon fishing line to a fence post. She stretches it out and shakes the end of the rope in her hand back and forth to produce waves on the line. The most efficient way for her to increase the wavelength is to
a. increase the tension on the hose and shake the end more times per second.
b. decrease the tension on the hose and shake the end more times per second.
c. increase the tension on the hose and shake the end fewer times per second.
d. decrease the tension on the hose and shake the end fewer times per second.
e. keep the tension and frequency the same but increase the length of the hose.

Answer 112

c. increase the tension on the hose and shake the end fewer times per second.

Question 113

Refer to Exhibit 16-1. Which of the graphs below shows a wave where the amplitude and the frequency are doubled?

Answer 113

Graph with 7 nodes

Question 114

Refer to Exhibit 16-1. Which of the graphs below shows a wave where the amplitude and frequency are each reduced in half?

Answer 114

Graph with 2 nodes (the smaller one)

Question 115

Refer to Exhibit 16-2. Which of the graphs below shows a wave where the frequency and wave velocity are both doubled?

Answer 115

Graph with 4 nodes (the smaller one)

Question 116

Refer to Exhibit 16-2. Which of the graphs below shows a wave where the frequency and wave velocity are both doubled?

Answer 116

Graph with 2 nodes

Question 117

Suppose that you were selected for a “Survivor”-type TV show. To help keep your group connected, you suggest that long vines can be tied together and used to transmit signals in cases of emergency. To get the signals to travel faster, you should
a. select lighter vines.
b. increase the tension on the vines.
c. hang weights from the vines at evenly spaced intervals.
d. do all of the above.
e. do (a) or (b) above, preferably both.

Answer 117

e. do (a) or (b) above, preferably both.

Question 118

Ariel claims that a pulse is described by the equation

  y(x,t) = 2/x^2-6.0xt + 9t^2+9 

where x and y are measured in cm and t in s. Miranda says that it is not possible to represent a pulse with this function because a wave must be a function of x + vt or x − vt. Which one, if either, is correct, and why?
a. Ariel, because x2 – 6.0xt + 9t2 = (x – 3.0t)2.
b. Ariel, because a pulse is not an infinite wave.
c. Miranda, because (x – 3.0t)2 is the same as (3.0t – x)2.
d. Miranda, because a pulse is not an infinite wave.
e. Miranda, because x^2-6.0xt + 9t^2 = x^2(1-6.00t/x + 9t^2/x^2) is infinite when x = 0.

Answer 118

a. Ariel, because x2 – 6.0xt + 9t2 = (x – 3.0t)2.

Question 119

The figure below represents a string which has a heavy section and a light section. The mass per unit length of the heavy section is 16 times as large as the mass per unit length of the light section. When the string is under tension, the speed of a pulse traveling in the heavy section is ____ times the speed of that same pulse traveling in the light section.

a. 1/16
b. 1/4
c. 1/2
d. 2
e. 4

Answer 119

b. 1/4

Question 120

To transmit four times as much energy per unit time along a string, you can
a. double the frequency.
b. double the amplitude.
c. increase the tension by a factor of 16.
d. do any one of the above.
e. do only (a) or (b) above.

Answer 120

d. do any one of the above

Question 121

The wave equation is written down in an exam as

  d^2y/dx^2 = v^2 d^2y/dt^2

From dimensional considerations we see that
a. v2 should be replaced by T/mew
b. v2 should be replaced by sqrt T/ mew
c. v2 should be replaced by v
d. v2 should be replaced by 1/v
e. v2 should be replaced by 1/v^2.

Answer 121

e. v2 should be replaced by 1/v^2.

Question 122

Refer to Exhibit 16-3. Rank the wave functions in order of the magnitude of the wave speeds, from least to greatest.
a. IV, II, I, III
b. IV = II, I, III
c. III, I, II, IV
d. IV, I, II, III
e. III, IV, II, I

Answer 122

b. IV = II, I, III

Question 123

Refer to Exhibit 16-3. Rank the wave functions in order of the magnitude of the frequencies of the waves, from least to greatest.
a. IV, II, I, III
b. IV = II, I, III
c. III, I, II, IV
d. IV, I, II, III
e. III, IV, II, I

Answer 123

a. IV, II, I, III

Question 124

Refer to Exhibit 16-3. Rank the wave functions in order of the magnitude of the wavelengths, from least to greatest.
a. IV, II, I, III
b. IV, I, II, III
c. I, II, III, IV
d. IV, II, III = I
e. I = III, II, IV

Answer 124

e. I = III, II, IV

Question 125

You are holding on to one end of a long string that is fastened to a rigid steel light pole. After producing a wave pulse that was 5 mm high and 4 cm wide, you want to produce a pulse that is 4 cm wide but 7 mm high. You must move your hand up and down once,
a. the same distance up as before, but take a shorter time.
b. the same distance up as before, but take a longer time.
c. a smaller distance up, but take a shorter time.
d. a greater distance up, but take a longer time.
e. a greater distance up, but take the same time.

Answer 125

e. a greater distance up, but take the same time.

Question 126

You are holding on to one end of a long string that is fastened to a rigid steel light pole. After producing a wave pulse that was 5 mm high and 4 cm wide, you want to produce a pulse that is 6 cm wide but still 5 mm high. You must move your hand up and down once,
a. the same distance up as before, but take a shorter time.
b. the same distance up as before, but take a longer time.
c. a smaller distance up, but take a shorter time.
d. a greater distance up, but take a longer time.
e. a greater distance up, but take the same time.

Answer 126

b. the same distance up as before, but take a longer time.

Question 127

You are holding on to one end of a long string that is fastened to a rigid steel light pole. After producing a wave pulse that was 5 mm high and 4 cm wide, you want to produce a pulse that is 6 cm wide and 7 mm high. You must move your hand up and down once,
a. the same distance up as before, but take a shorter time.
b. the same distance up as before, but take a longer time.
c. a smaller distance up, but take a shorter time.
d. a greater distance up, but take a longer time.
e. a greater distance up, but take the same time.

Answer 127

d. a greater distance up, but take a longer time.

Question 128

Earthquake waves are classified as P waves and S waves. Which of the following statements is true about these waves?
a. The P wave is transverse as is the S wave.
b. The P wave is longitudinal as is the S wave.
c. The P wave is transverse and the S wave is longitudinal.
d. The P wave is longitudinal and the S wave is transverse.
e. Both the P and S waves are mixtures of longitudinal and transverse waves.

Answer 128

d. The P wave is longitudinal and the S wave is transverse.

Question 129

A pulse is described by in SI units. What is the velocity of the pulse?
a. 3 m/s in the +x direction
b. 2 m/s in the −x direction
c. 2 m/s in the +x direction
d. 4 m/s in the −x direction
e. 4 m/s in the +x direction

Answer 129

b. 2 m/s in the −x direction

Question 130

The equation y = Asin(kx-wt + pi/2) is the same as
a. y = -Asin(kx-wt+pi/2)
b. y = Acos(kx-wt)
c. y = -Acos(kx-wt)
d. y = -Asin(kx-wt-pi/2)
e. y = Asin(kx-wt+3pi/2)

Answer 130

b. y = Acos(kx-wt)

Question 131

What is the expression for the transverse velocity of the wave in a string given by y = Asin(kx-wt)?
a. v = Acos(kx-wt)
b. v = kAcos(kx-wt)
c. v = -kAcos(kx-wt)
d. v = -wAcos(kx-wt)
e. v = wAcos(kx-wt)

Answer 131

d. v = -wAcos(kx-wt)

Question 132

If the breakers at a beach are separated by 5.0 m and hit shore with a frequency of 0.20 Hz, with what speed are they traveling?

Answer 132

1.0 m/s

Question 133

Bats can detect small objects such as insects that are of a size approximately that of one wavelength. If bats emit a chirp at a frequency of 60 kHz, and the speed of sound in air is 340 m/s, what is the smallest size insect they can detect?

Answer 133

5.7 mm

Question 134

A circus performer stretches a tightrope between two towers. He strikes one end of the rope and sends a wave along it toward the other tower. He notes that it takes 0.8 s for the wave to travel the 20 m to the opposite tower. If one meter of the rope has a mass of 0.35 kg, find the tension in the tightrope.

Answer 134

219 N

Question 135

The velocity of sound in sea water is 1.53 × 10^3 m/s. Find the bulk modulus (in N/m^2) of sea water if its density is 1.03 × 10^3 kg/m3.
a. 2.57 × 10^9
b. 2.19 × 10^9
c. 2.04 × 10^9
d. 2.41 × 10^9
e. 2.82 × 10^9

Answer 135

d. 2.41 × 10^9

Question 136

A sculptor strikes a piece of marble with a hammer. Find the speed of sound through the marble (in km/s). (The Young’s modulus is 50 × 109 N/m2 and its density is 2.7 × 103 kg/m3.)
a. 5.1
b. 4.3
c. 3.5
d. 1.3
e. 1.8

Answer 136

b. 4.3

Question 137

The Young’s modulus for aluminum is 7.02 × 10^10 N/m2. If the speed of sound in aluminum is measured to be 5.10 km/s, find its density (in kg/m3).
a. 11.3 × 10^3
b. 7.80 × 10^3
c. 2.70 × 10^3
d. 29.3 × 10^3
e. 1.40 × 10^3

Answer 137

c. 2.70 × 10^3

Question 138

It is possible to hear an approaching train before you can see it by listening to the sound wave through the track. If the elastic modulus is 2.0 × 1011 N/m2 and the density of steel is 7.8 × 103 kg/m3, approximately how many times faster is the speed of sound in the track than in air? (vair ≈ 340 m/s.)
a. 20
b. 5
c. 10
d. 15
e. 25

Answer 138

d. 15

Question 139

Calculate the pressure amplitude (in N/m2) of a 500 Hz sound wave in helium if the displacement amplitude is equal to 5.0 × 10^−8 m. (ρ = 0.179 kg/m3, v = 972 m/s.)
a. 3.5 × 10^−2
b. 1.6 × 10^−2
c. 2.7 × 10^−2
d. 4.2 × 10^−2
e. 2.0 × 10^−2

Answer 139

c. 2.7 × 10−2

Question 140

Calculate the displacement amplitude (in m) of a 20 kHz sound wave in helium if it has a pressure amplitude of 8.0 × 10^−3 N/m2. (ρ = 0.179 kg/m3, v = 972 m/s.)
a. 2.9 × 10^−10
b. 3.7 × 10^−10
c. 7.8 × 10^−9
d. 2.4 × 10^−9
e. 1.9 × 10^−10

Answer 140

b. 3.7 × 10^−10

Question 141

The variation in the pressure of helium gas, measured from its equilibrium value, is given by ΔP = 2.9 × 10^−5 cos (6.20x − 3 000t) where x and t have units m and s, and ΔP is measured in N/m2. Determine the frequency (in Hz) of the wave.
a. 1 500
b. 477
c. 1.01
d. 0.32
e. 239

Answer 141

b. 477

Question 142

The variation in the pressure of helium gas, measured from its equilibrium value, is given by ΔP = 2.9 × 10−5 cos (6.20x − 3 000t) where x and t have units m and s, and ΔP is measured in N/m2. Determine the wavelength (in m) of the wave.
a. 1 500
b. 0.32
c. 477
d. 1.01
e. 0.50

Answer 142

d. 1.01

Question 143

The variation in the pressure of helium gas, measured from its equilibrium value, is given by ΔP = 2.9 × 10^−5 cos (6.20x − 3 000t) where x and t have units m and s. Determine the speed (in m/s) of the wave.
a. 1 515
b. 153
c. 484
d. 828
e. 101

Answer 143

c. 484

Question 144

Determine the intensity (in W/m2) of a harmonic longitudinal wave with a pressure amplitude of 8.0 × 10^−3 N/m2 propagating down a tube filled with helium. (ρ = 0.179 kg/m3, v = 972 m/s.)
a. 3.7 × 10^−7
b. 1.8 × 10^−7
c. 9.2 × 10^−8
d. 4.6 × 10^−8
e. 1.5 × 10^−9

Answer 144

b. 1.8 × 10−7

Question 145

Calculate the intensity level in dB of a sound wave that has an intensity of 15 × 10^−4 W/m2.
a. 20
b. 200
c. 92
d. 9
e. 10

Answer 145

c. 92

Question 146

A jet plane has a sound level of 150 dB. What is the intensity in W/m2?
a. 1
b. 100
c. 10
d. 1 000
e. 10 000

Answer 146

d. 1 000

Question 147

By what factor will an intensity change when the corresponding sound level increases by 3 dB?
a. 3
b. 0.5
c. 2
d. 4
e. 0.3

Answer 147

c. 2

Question 148

By what factor is the intensity of sound at a rock concert louder than that of a whisper when the two intensity levels are 120 dB and 20 dB respectively?
a. 10^12
b. 10^8
c. 10^6
d. 10^10
e. 10^11

Answer 148

d. 10^10

Question 149

A point source emits sound with a power output of 100 watts. What is the intensity (in W/m2) at a distance of 10.0 m from the source?
a. 7.96 × 10^−2
b. 7.96 × 10^−1
c. 7.96 × 10^0
d. 7.96 × 10^1
e. 7.96 × 10^−3

Answer 149

a. 7.96 × 10^−2

Question 150

A point source emits sound waves with a power output of 100 watts. What is the sound level (in dB) at a distance of 10 m?
a. 139
b. 119
c. 129
d. 109
e. 10

Answer 150

d. 109

Question 151

A car approaches a stationary police car at 36 m/s. The frequency of the siren (relative to the police car) is 500 Hz. What is the frequency (in Hz) heard by an observer in the moving car as he approaches the police car? (Assume the velocity of sound in air is 343 m/s.)
a. 220
b. 448
c. 526
d. 552
e. 383

Answer 151

d. 552

Question 152

A car moving at 36 m/s passes a stationary police car whose siren has a frequency of 500 hz. What is the change in the frequency (in Hz) heard by an observer in the moving car as he passes the police car? (The speed of sound in air is 343 m/s.)
a. 416
b. 208
c. 105
d. 52
e. 552

Answer 152

c. 105

Question 153

A truck moving at 36 m/s passes a police car moving at 45 m/s in the opposite direction. If the frequency of the siren relative to the police car is 500 Hz, what is the frequency heard by an observer in the truck as the police car approaches the truck? (The speed of sound in air is 343 m/s.)
a. 396
b. 636
c. 361
d. 393
e. 617

Answer 153

b. 636

Question 154

A truck moving at 36 m/s passes a police car moving at 45 m/s in the opposite direction. If the frequency of the siren is 500 Hz relative to the police car, what is the frequency heard by an observer in the truck after the police car passes the truck? (The speed of sound in air is 343 m/s.)
a. 361
b. 636
c. 393
d. 396
e. 383

Answer 154

d. 396

Question 155

A truck moving at 36 m/s passes a police car moving at 45 m/s in the opposite direction. If the frequency of the siren is 500 Hz relative to the police car, what is the change in frequency (in Hz) heard by an observer in the truck as the two vehicles pass each other? (The speed of sound in air is 343 m/s.)
a. 242
b. 238
c. 240
d. 236
e. 234

Answer 155

c. 240

Question 156

How fast (in m/s) is the Concorde moving if it reaches Mach 1.5? (The speed of sound in air is 344 m/s.)
a. 229
b. 516
c. 416
d. 728
e. 858

Answer 156

b. 516

Question 157

A stone is thrown into a quiet pool of water. With no fluid friction, the amplitude of the waves falls off with distance r from the impact point as
a. 1/r3
b. 1/r2
c. 1/r3/2
d. 1/r1/2
e. 1/r

Answer 157

d. 1/r1/2

Question 158

A wave generated in a medium is a longitudinal wave when
a. there is a net transport of matter by the wave.
b. the molecules of the medium are unable to exert forces on each other.
c. molecular displacements are parallel to the wave velocity.
d. molecular displacements are perpendicular to the wave velocity.
e. the density of the medium is less than the density of water.

Answer 158

c. molecular displacements are parallel to the wave velocity.

Question 159

When you hear the horn of a car that is approaching you, the frequency that you hear is larger than that heard by a person in the car because for the sound you hear
a. wave crests are farther apart by the distance the car travels in one period.
b. wave crests are closer together by the distance the car travels in one period.
c. the car gets ahead of each wave crest before it emits the next one.
d. the speed of sound in air is increased by the speed of the car.
e. a speeding car emits more wavecrests in each period.

Answer 159

b. wave crests are closer together by the distance the car travels in one period.

Question 160

While you are sounding a tone on a toy whistle, you notice a friend running toward you. If you want her to hear the same frequency that you hear even though she is approaching, you must
a. stay put.
b. run towards her at the same speed.
c. run away from her at the same speed.
d. stay put and play a note of higher frequency.
e. run towards her and play a note of higher frequency.

Answer 160

c. run away from her at the same speed.

Question 161

To decrease the intensity of the sound you are hearing from your speaker system by a factor of 36, you can
a. reduce the amplitude by a factor of 12 and increase your distance from the speaker by a factor of 3.
b. reduce the amplitude by a factor of 4 and increase your distance from the speaker by a factor of 3.
c. reduce the amplitude by a factor of 2 and increase your distance from the speaker by a factor of 3.
d. reduce the amplitude by a factor of 3 and increase your distance from the speaker by a factor of 4.
e. reduce the amplitude by a factor of 3 and increase your distance from the speaker by a factor of 12.

Answer 161

c. reduce the amplitude by a factor of 2 and increase your distance from the speaker by a factor of 3.

Question 162

A person standing in the street is unaware of a bird dropping that is falling from a point directly above him with increasing velocity. If the dropping were producing sound of a fixed frequency, as it approaches the person would hear the sound
a. drop in frequency.
b. stay at the same frequency.
c. increase in frequency.
d. decrease in loudness.
e. stay at the same loudness.

Answer 162

c. increase in frequency.

Question 163

(Do not try the following: it could kill you. This question is only about a hypothetical possibility.) If you were standing below an object emitting a fixed frequency sound falling at terminal velocity, as it approached you, you would hear the sound
a. drop in frequency.
b. stay at the same frequency.
c. increase in frequency.
d. decrease in loudness.
e. stay at the same loudness.

Answer 163

b. stay at the same frequency.

Question 164

A spherical wave has the form

phi(r,t) = (0.002 cm/r)sin(8pi/m * -2720pi/s t)

The amplitude of the wave a distance r from the source is
a. 0.002 cm.
b. 0.002 cm/sqrt r
c. 0.002 cm/r
d. (0.002 cm)^2/r
e. 0.002 cm /r^2

Answer 164

c. 0.002 cm/r

Question 165

A spherical wave has the form

phi(r,t) = (0.002 cm/r)sin(8pi/m * -2720pi/s t)

The wavelength of the wave is
a. 0.25 m.
b. 0.50 m.
c. 4.0 m.
d. 8.0 m.
e. 4.0π m.

Answer 165

a. 0.25 m.

Question 166

A spherical wave has the form

phi(r,t) = (0.002 cm/r)sin(8pi/m * -2720pi/s t)

The frequency of the wave (in Hz) is
a. 3.68 × 10−4.
b. 7.35 × 10−4.
c. 1 360.
d. 2 720.
e. 2 720π.

Answer 166

c. 1 360.

Question 167

A spherical wave has the form

phi(r,t) = (0.002 cm/r)sin(8pi/m * -2720pi/s t)

The velocity of the wave (in m/s) is
a. 0.005 88.
b. 16.0
c. 340.
d. 1 360.
e. 2 720.

Answer 167

c. 340.

Question 168

A boy has climbed to the top of a 6.00 m tall tree. When he shouts, the sound waves have an intensity of 0.250 W/m^2 at a 1.00 m distance from the top of the tree. The ratio of intensity at the base of the tree to the intensity 1.00 m from the top of the tree is
a. 1/36
b. 1/25
c. 1/6
d. 1/5
e. 1/sqrt6

Answer 168

a. 1/36

Question 169

Which of the following does not have a precise definition in terms of the physical properties of sound waves?
a. frequency
b. intensity
c. loudness
d. sound level
e. wavelength

Answer 169

c. loudness

Question 170

A friend hands you an equation sheet with the following equation for the Doppler effect: . This version of the equation is correct with signs as given only if
a. the observer and source are approaching each other.
b. the observer is approaching the source while the source is moving away from the observer.
c. the observer is moving away from the source while the source is approaching the observer.
d. the observer and source are moving away from each other.
e. the observer and source are moving in perpendicular directions.

Answer 170

d. the observer and source are moving away from each other.

Question 171

Two harmonic waves are described by

  y1 = (3 m)sin(4/m x - 700/s t)
  y2 = (3 m)sin(4/m x - 700/s t -2) 

What is the amplitude of the resultant wave?
a. 8.0 m
b. 4.3 m
c. 6.0 m
d. 3.2 m
e. 3.0 m

Answer 171

d. 3.2 m

Question 172

Two harmonic waves are described by

  y1 = (4 m)sin(8/m x - 300/s t)
  y2 = (4 m)sin(8/m x - 300/s t -2) 

What is the frequency (in Hz) of the resultant wave?
a. 300
b. 48
c. 8
d. 0.8
e. 150

Answer 172

b. 48

Question 173

Two harmonic waves are described by

  y1 = (5 m)sin(6/m x - 900/s t)
  y2 = (5 m)sin(6/m x - 900/s t-2) 

What is the wavelength of the resultant wave?
a. 3 m
b. 2 m
c. 1 m
d. 4 m
e. 6 m

Answer 173

c. 1 m

Question 174

Two harmonic waves are described by

  y1 = (7 m)sin(5/m x - 100/s t)
  y2 = (7 m)sin(5/m x - 100/s t+2) 

What is the phase (in rad) of the resultant wave when x = t = 0?
a. 3
b. 0
c. 2
d. 1
e. 4

Answer 174

d. 1

Question 175

The path difference between two waves is 5m. If the wavelength of the waves emitted by the two sources is 4m, what is the phase difference (in degrees)?
a. 90
b. 400
c. 1.57
d. 7.85
e. 15

Answer 175

a. 90

Question 176

Two harmonic waves are described by

  y1 = (3 cm)sin(8.0/m x + 2.0/s t) 
  y2 = (3 cm)sin(8.0/m x - 2.0/s t)

What is the magnitude of the speed (in m/s) of the two traveling waves?
a. 16
b. 4.0
c. 8.0
d. 0.25
e. 2.0

Answer 176

d. 0.25

Question 177

Two harmonic waves are described by

  y1 = (6 cm)sin(pi(8/m x + 2/s t)) 
  y2 = (6 cm)sin(pi(8/m x - 2/s t)) 

From the choices given, determine the smallest positive value of x (in cm) corresponding to a node of the resultant standing wave.
a. 3
b. 0.25
c. 0
d. 6
e. 1.5

Answer 177

c. 0

Question 178

Two harmonic waves are described by

  y1 = (6.00 cm)sin(pi(2.00/m x + 3.00/s t)) 
  y2 = (6.00 cm)sin(pi(2.00/m x - 3.00/s t)) 

What is the magnitude of the displacement (in cm) of this wave at x = 3 cm and t = 5 sec?
a. 12.0
b. 3.00
c. 6.00
d. 2.25
e. 0

Answer 178

d. 2.25

Question 179

Two harmonic waves traveling in opposite directions interfere to produce a standing wave described by y = 3 sin (2x) cos 5t where x is in m and t is in s. What is the wavelength of the interfering waves?
a. 3.14 m
b. 1.00 m
c. 6.28 m
d. 12.0 m
e. 2.00 m

Answer 179

a. 3.14 m

Question 180

Two harmonic waves traveling in opposite directions interfere to produce a standing wave described by y = 4 sin (5x) cos (6t) where x is in m and t is in s. What is the approximate frequency of the interfering waves?
a. 3 Hz
b. 1 Hz
c. 6 Hz
d. 12 Hz
e. 5 Hz

Answer 180

b. 1 Hz

Question 181

Two harmonic waves traveling in opposite directions interfere to produce a standing wave described by y = 2 sin (4x) cos (3t) where x is in m and t is in s. What is the speed (in m/s) of the interfering waves?
a. 0.75
b. 0.25
c. 1.3
d. 12
e. 3.0

Answer 181

a. 0.75

Question 182

Two harmonic waves traveling in opposite directions interfere to produce a standing wave described by y = 2 sin (πx) cos (3πt) where x is in m and t is in s. What is the distance (in m) between the first two antinodes?
a. 8
b. 2
c. 4
d. 1
e. 0.5

Answer 182

d. 1

Question 183

A string is stretched and fixed at both ends, 200 cm apart. If the density of the string is 0.015 g/cm, and its tension is 600 N, what is the wavelength (in cm) of the first harmonic?
a. 600
b. 400
c. 800
d. 1 000
e. 200

Answer 183

b. 400

Question 184

A string is stretched and fixed at both ends, 200 cm apart. If the density of the string is 0.015 g/cm, and its tension is 600 N, what is the fundamental frequency?
a. 316 Hz
b. 632 Hz
c. 158 Hz
d. 215 Hz
e. 79 Hz

Answer 184

c. 158 Hz

Question 185

A stretched string is observed to vibrate in three equal segments when driven by a 480 Hz oscillator. What is the fundamental frequency of vibration for this string?
a. 480 Hz
b. 320 Hz
c. 160 Hz
d. 640 Hz
e. 240 Hz

Answer 185

c. 160 Hz

Question 186

A clarinet behaves like a tube closed at one end. If its length is 1.0 m, and the velocity of sound is 344 m/s, what is its fundamental frequency (in Hz)?
a. 264
b. 140
c. 86
d. 440
e. 172

Answer 186

c. 86

Question 187

An organ pipe open at both ends has a radius of 4.0 cm and a length of 6.0 m. What is the frequency (in Hz) of the third harmonic? (Assume the velocity of sound is 344 m/s.)
a. 76
b. 86
c. 54
d. 28
e. 129

Answer 187

b. 86

Question 188

A vertical tube one meter long is open at the top. It is filled with 75 cm of water. If the velocity of sound is 344 m/s, what will the fundamental resonant frequency be (in Hz)?
a. 3.4
b. 172
c. 344
d. 1.7
e. 688

Answer 188

c. 344

Question 189

A length of organ pipe is closed at one end. If the speed of sound is 344 m/s, what length of pipe (in cm) is needed to obtain a fundamental frequency of 50 Hz?
a. 28
b. 86
c. 344
d. 172
e. 688

Answer 189

d. 172

Question 190

Two tuning forks with frequencies 264 and 262 Hz produce “beats”. What is the beat frequency (in Hz)?
a. 4
b. 2
c. 1
d. 3
e. 0 (no beats are produced)

Answer 190

b. 2

Question 191

Two instruments produce a beat frequency of 5 Hz. If one has a frequency of 264 Hz, what could be the frequency of the other instrument?
a. 269 Hz
b. 254 Hz
c. 264 Hz
d. 5 Hz
e. 274 Hz

Answer 191

a. 269 Hz

Question 192

Two waves are described by

 y1 = 6 cos 180t and y2 = 6 cos 186t, (both in meters).

With what angular frequency does the maximum amplitude of the resultant wave vary with time?
a. 366 rad/s
b. 6 rad/s
c. 3 rad/s
d. 92 rad/s
e. 180 rad/s

Answer 192

c. 3 rad/s

Question 193

Two waves are described by

 y1 = 6 cos 180t and y2 = 6 cos 186t, (both in meters).

What effective frequency does the resultant vibration have at a point?
a. 92 Hz
b. 183 Hz
c. 6 Hz
d. 3 Hz
e. 366 Hz

Answer 193

b. 183 Hz

Question 194

An organ pipe open at both ends is 1.5 m long. A second organ pipe that is closed at one end and open at the other is 0.75 m long. The speed of sound in the room is 330 m/s. Which of the following sets of frequencies consists of frequencies which can be produced by both pipes?
a. 110 Hz, 220 Hz, 330 Hz
b. 220 Hz, 440 Hz, 660 Hz
c. 110 Hz, 330 Hz, 550 Hz
d. 330 Hz, 440 Hz, 550 Hz
e. 220 Hz, 660 Hz, 1 100 Hz

Answer 194

c. 110 Hz, 330 Hz, 550 Hz

Question 195

Two strings are respectively 1.00 m and 2.00 m long. Which of the following wavelengths, in meters, could represent harmonics present on both strings?
a. 0.800, 0.670, 0.500
b. 1.33, 1.00, 0.500
c. 2.00, 1.00, 0.500
d. 2.00, 1.33, 1.00
e. 4.00, 2.00, 1.00

Answer 195

c. 2.00, 1.00, 0.500

Question 196

Two point sources emit sound waves of 1.0-m wavelength. The sources, 2.0 m apart, as shown below, emit waves which are in phase with each other at the instant of emission. Where, along the line between the sources, are the waves out of phase with each other by π radians?

a. x = 0, 1.0 m, 2.0 m
b. x = 0.50 m, 1.5 m
c. x = 0.50 m, 1.0 m, 1.5 m
d. x = 0.75 m, 1.25 m
e. x = 0.25 m, 0.75 m, 1.25 m, 1.75 m

Answer 196

d. x = 0.75 m, 1.25 m

Question 197

Two identical strings have the same length and same mass per unit length. String B is stretched with four times as great a tension as that applied to string A. Which statement is correct for all n harmonics on the two strings, n = 1, 2, 3…?
a. fn,B = 1/4fn,A
b. fn,B = 1/2fn,A
c. fn,B = sqrt2 fn,A
d. fn,B = 2fn,A.
e. fn,B = 4fn,A.

Answer 197

d. fn,B = 2fn,A.

Question 198

The superposition of two waves

  y1 = (0.006 cm)cos[2pi(156/s t)] and
  y2 = (0.006 cm)cos[2pi(150/s t)] 

at the location x = 0 in space results in
a. beats at a beat frequency of 3 Hz.
b. a pure tone at a frequency of 153 Hz.
c. a pure tone at a frequency of 156 Hz.
d. beats at a beat frequency of 6 Hz in a 153 Hz tone.
e. a tone at a frequency of 156 Hz, as well as beats at a beat frequency of 6 Hz in a 153 Hz tone.

Answer 198

d. beats at a beat frequency of 6 Hz in a 153 Hz tone.

Question 199

The superposition of two waves,

  y1 = (2*10^-8 m)sin[pi(x/2m - 170/s t)] and
  y2 = (2*10^-8 m)sin[pi(x/2m - 170/s t - 1/2)] 

results in a wave with a phase angle of
a. 0 rad.
b. 0.5 rad.
c. pi/4 rad.
d. pi/2 rad.
e. π rad.

Answer 199

c. pi/4 rad.

Question 200

The superposition of two waves,

  y1 = (2*10^-8 m)sin[pi(x/2m - 170/s t)] and
  y2 = (2*10^-8 m)sin[pi(x/2m - 170/s t - 1/2)] 

results in a wave with a wavelength of

a. pi/2 m.
b. 2 m.
c. π m.
d. 4 m.
e. 4π m.

Answer 200

d. 4 m.

Question 201

The superposition of two waves,

  y1 = (2*10^-8 m)sin[pi(x/2m - 170/s t)] and
  y2 = (2*10^-8 m)sin[pi(x/2m - 170/s t - 1/2)] 

results in a wave with a frequency of
a. 85 Hz.
b. 170 Hz.
c. 85π Hz.
d. 340 Hz.
e. 170π Hz.

Answer 201

a. 85 Hz.

Question 202

In a standing wave, not necessarily at the fundamental frequency, on a string of length L, the distance between nodes is
a. λ/4.
b. λ/2.
c. λ.
d. L/4.
e. L/2.

Answer 202

b. λ/2.

Question 203

Which of the following wavelengths could NOT be present as a harmonic on a 2 m long string?
a. 4 m
b. 2 m
c. 1 m
d. 0.89 m
e. 0.5 m

Answer 203

d. 0.89 m

Question 204

Which of the following wavelengths could NOT be present as a standing wave in a 2 m long organ pipe open at both ends?
a. 4 m
b. 2 m
c. 1 m
d. 0.89 m
e. 0.5 m

Answer 204

d. 0.89 m

Question 205

Which of the following frequencies could NOT be present as a standing wave in a 2m long organ pipe open at both ends? The fundamental frequency is 85 Hz.
a. 85 Hz.
b. 170 Hz.
c. 255 Hz.
d. 340 Hz.
e. 382 Hz.

Answer 205

e. 382 Hz.

Question 206

An observer stands 3 m from speaker A and 4 m from speaker B. Both speakers, oscillating in phase, produce 170 Hz waves. The speed of sound in air is 340 m/s. What is the phase difference (in radians) between the waves from A and B at the observer’s location, point P?

a. 0
b. pi/2
c. π
d. 2π
e. 4π

Answer 206

c. π

Question 207

As shown below, a garden room has three walls, a floor and a roof, but is open to the garden on one side. The wall widths are L and w. The roof height is h. When traveling sound waves enter the room, standing sound waves can be present in the room if the wavelength of the standing waves is

a. 2L/n, where n is a positive integer.
b. 4w/n, where n is an odd integer.
c. h/n, where n is an even integer.
d. in all cases listed above.
e. given by (a) or (b) above, but not by (c).

Answer 207

e. given by (a) or (b) above, but not by (c).

Question 208

Transverse waves y1 = A1 sin(k1x − ω1t) and y2 = A2 sin(k2x − ω2t), with A2 > A1, start at opposite ends of a long rope when t = 0. The magnitude of the maximum displacement, y, of the rope at any point is
a. A1 − A2.
b. A2 − A1.
c. A1 + A2.
d. (A1-A2)k1/k2
e. (A2-A1)k2/k1

Answer 208

c. A1 + A2.

Question 209

Two speakers in an automobile emit sound waves that are in phase at the speakers. One speaker is 40 cm ahead of and 30 cm to the left of the driver’s left ear. The other speaker is 50 cm ahead of and 120 cm to the right of the driver’s right ear. Which of the following wavelengths is(are) in phase at the left ear for the speaker on the left and the right ear for the speaker on the right?
a. 10 cm
b. 20 cm
c. 650 cm
d. All of the wavelengths listed above.
e. Only the wavelengths listed in (a) and (b).

Answer 209

e. Only the wavelengths listed in (a) and (b).

Question 210

A very long string is tied to a rigid wall at one end while the other end is attached to a simple harmonic oscillator. Which of the following can be changed by changing the frequency of the oscillator?
a. The speed of the waves traveling along the string.
b. The tension in the string.
c. The wavelength of the waves on the string.
d. All of the above.
e. None of the above.

Answer 210

c. The wavelength of the waves on the string.

Question 211

When two organ pipes open at both ends sound a perfect fifth, such as two notes with fundamental frequencies at 440 Hz and 660 Hz, both pipes produce overtones. Which choice below correctly describes overtones present in both pipes?
a. 440, 880 and 1 320 Hz.
b. 660, 1 320 and 1 980 Hz.
c. 880, 1 320 and 1 760 Hz.
d. 1 320, 2 640 and 3 960 Hz.
e. They have no overtones in common.

Answer 211

d. 1 320, 2 640 and 3 960 Hz.

Question 212

When two organ pipes each closed at one end sound a perfect fifth, such as two notes with fundamental frequencies at 440 Hz and 660 Hz, both pipes produce overtones. Which choice below correctly describes overtones present in both pipes?
a. 440, 880 and 1 320 Hz.
b. 660, 1 320 and 1 980 Hz.
c. 880, 1 320 and 1 760 Hz.
d. 1 320, 2 640 and 3 960 Hz.
e. They have no overtones in common.

Answer 212

e. They have no overtones in common.

Question 213

Two organ pipes, a pipe of fundamental frequency 440 Hz, closed at one end, and a pipe of fundamental frequency 660 Hz, open at both ends, produce overtones. Which choice below correctly describes overtones present in both pipes?
a. After the first overtone of each pipe, every second overtone of the first pipe matches every second overtone of the second pipe.
b. After the first overtone of each pipe, every second overtone of the first pipe matches every third overtone of the second pipe.
c. After the first overtone of each pipe, every third overtone of the first pipe matches every second overtone of the second pipe.
d. After the first overtone of each pipe, every second overtone of the first pipe matches every fourth overtone of the second pipe.
e. After the first overtone of each pipe, every third overtone of the first pipe matches every fourth overtone of the second pipe.

Answer 213

e. After the first overtone of each pipe, every third overtone of the first pipe matches every fourth overtone of the second pipe.

Question 214

Refer to Exhibit 18-1. The phase difference in radians between points A and B is
a. 0.
b. pi/4
c. pi/2
d. π.
e. 3pi/2

Answer 214

a. 0.

Question 215

Refer to Exhibit 18-1. The phase difference in radians between points A and C is
a. 0.
b. pi/2
c. π.
d. 3pi/2
e. 2π

Answer 215

e. 2π

Question 216

Refer to Exhibit 18-1. The phase difference in radians between points A and D is
a. π.
b. 2π.
c. 3π.
d. 4π.
e. 5π.

Answer 216

c. 3π.

Question 217

A harmonic longitudinal wave propagating down a tube filled with a compressible gas has the form s(x, t) = sm cos (kx − ωt). Its velocity can be obtained from
a. ω/k
b. k/ω
c. k
d. ω
e. ωk

Answer 217

a. ω/k

Question 218

Drummers like to have high-pitched cymbals that vibrate at high frequencies. To obtain the highest frequencies, a cymbal of a fixed size should be made of a material
a. with a low Young’s modulus and a low density.
b. with a low Young’s modulus and a high density.
c. with a high Young’s modulus and a low density.
d. with a high Young’s modulus and a high density.
e. composed of a metal-plastic laminate.

Answer 218

c. with a high Young’s modulus and a low density.

Question 219

A fire engine approaches a wall at 5 m/s while the siren emits a tone of 500 Hz frequency. At the time, the speed of sound in air is 340 m/s. How many beats per second do the people on the fire engine hear?
a. 0
b. 15
c. 29
d. 63
e. 250

Answer 219

b. 15

Question 220

The figure below shows the positions of particles in a longitudinal standing wave. One quarter period later the particle distribution is shown in

Answer 220

longest consecutive chain of dots

Question 221

A string with a fixed frequency vibrator at one end is undergoing resonance with 4 antinodes when under tension T1. When the tension is slowly increased the resonance condition disappears until tension T2 is reached, there being no resonances occurring between these two tensions. How many antinodes are there in this new resonance?
a. 3
b. 4, since all resonances in this situation have the same number of nodes
c. 5
d. 2, since resonances only involve whole wavelengths
e. 6, since resonances only involve whole wavelength

Answer 221

a. 3

Question 222

A string with a fixed frequency vibrator at one end is subjected to varying tensions. When the tension is 20 N, a resonance with 3 antinodes results. What tension would cause a resonance with 2 antinodes in this string?
a. 30 N
b. 45 N
c. 80 N
d. 8.9 N
e. 13 N

Answer 222

b. 45 N

Question 223

Tuning forks #1, #2, and #3 each have slightly different frequencies.When #1 and #2 are sounded together, a beat frequency of 3 Hz results. When #2 and #3 are sounded together, a beat frequency of 5 Hz results. If the frequency of #1 is 100 Hz, which of the following cannot be the frequency of #3?
a. 92 Hz
b. 95 Hz
c. 98 Hz
d. 102 Hz
e. 108 Hz

Answer 223

b. 95 Hz

Question 224

Superposition of waves can occur
a. in transverse waves.
b. in longitudinal waves.
c. in sinusoidal waves.
d. in all of the above.
e. only in (a) and (c) above.

Answer 224

d. in all of the above.

Question 225

Two pulses are traveling towards each other at 10 cm/s on a long string at t = 0 s, as shown below.

Which diagram below correctly shows the shape of the string at 0.5 s?

Answer 225

square 3 cm long

Question 226

Two ropes are spliced together as shown.

A short time after the incident pulse shown in the diagram reaches the splice, the rope’s appearance will be that in

Answer 226

small speed bump and large speed bump

Question 227

Two ropes are spliced together as shown.

A short time after the incident pulse shown in the diagram reaches the splice, the rope’s appearance will be that in

Answer 227

small divot and then large speed bump

Question 228

A student wants to establish a standing wave on a wire 1.8 m long clamped at both ends. The wave speed is 540 m/s. What is the minimum frequency she should apply to set up standing waves?

Answer 228

150 Hz

Question 229

Find the frequencies of the first three harmonics of a 1.0-m long string which has a mass per unit length of 2.0 × 10−3 kg/m and a tension of 80 N when both ends are fixed in place.

Answer 229

100 Hz, 200 Hz, 300 Hz

Question 230

A steel wire in a piano has a length of 0.700 m and a mass of 4.30 grams. To what tension must this wire be stretched to make the fundamental frequency correspond to middle C, (fc = 261.6 Hz)?

Answer 230

824 N

Question 231

A boat sounds a fog horn on a day when both the sea water and the air temperature are 25.0° C. The speed of sound in sea water is 1 533 m/s. How much earlier (in s) does a dolphin 1 000 m from the source hear the sound than a person in a boat that is also 1 000 m distant? (Ignore the time it takes the sound to reach the water surface.)
a. 0.652
b. 2.12
c. 2.24
d. 2.77
e. 2.90

Answer 231

c. 2.24

Question 232

A source of sound waves is placed at the center of a very large sound-reflecting wall. The source emits 0.500 W of power. Two meters from the source the intensity in W/m2 is
a. 9.95 × 10^−3.
b. 1.99 × 10^−2.
c. 0.313.
d. 0.399.
e. 0.625.

Answer 232

b. 1.99 × 10^−2.

Question 233

On a day when the speed of sound in the upper air is 320 m/s, you fly coast to coast in the United States, a distance of about 4 850 km, in about one hour, if the Mach number for the speed of your airplane is about
a. 1.
b. 2
c. 3
d. 4
e. 5.

Answer 233

d. 4

Question 234

The fundamental frequency of a above middle C on the piano is 440 Hz. This is the tenor high A, but a convenient note in the mid-range of women’s voices. When we calculate the wavelength, we find that it is
a. much shorter than the length of either a man’s or woman’s lips.
b. shorter than the length of a man’s lips, but about the length of a woman’s lips.
c. longer than a woman’s lips, but about the length of a man’s lips.
d. much longer than the length of either a man’s or a woman’s lips.
e. about the same length as either a man’s or woman’s lips.

Answer 234

d. much longer than the length of either a man’s or a woman’s lips.

Question 235

If a supersonic plane is flying at increasing speed as the temperature decreases, what happens to the Mach number in this instance?
a. It stays the same.
b. It increases.
c. It decreases.
d. It can do any of the above.
e. It can do either (a) or (b) but not (c).

Answer 235

b. It increases.

Question 236

If a plane is flying at a speed so that the apex half-angle of its shockwave is 30°, what is its speed if the speed of sound is 320 m/s?
a. 960 m/s
b. 640 m/s
c. 320 m/s
d. 160 m/s
e. Choose this answer if a shock wave cannot form in this situation.

Answer 236

b. 640 m/s

Question 237

A speaker is producing 30 W of sound. At which of the following frequencies would it sound the loudest?
a. 50 Hz
b. 100 Hz
c. 500 Hz
d. 1 000 Hz
e. 10 000 Hz

Answer 237

d. 1 000 Hz

Question 238

A bat, flying at 5.00 m/s, emits a chirp at 40.0 kHz. If this sound pulse is reflected by a wall, what is the frequency of the echo received by the bat? (vsound = 340 m/s.)

Answer 238

41.2 kHz

Question 239

A microphone in the ocean is sensitive to the sounds emitted by porpoises. To produce a usable signal, sound waves striking the microphone must have an intensity of 1.02 × 10−11 W/m2. If porpoises emit sounds with a power of 0.049 9 W, how far away can a porpoise be and still be heard? Disregard absorption of sound waves by the water.

Answer 239

19.7 km

Question 240

An airplane traveling at half the speed of sound emits sound at a frequency of 5 000 Hz. At what frequency does a stationary listener hear the sound as the plane approaches, and after it passes by? Assume the airplane is not flying very high.

Answer 240

10000 Hz, 3333 Hz

Question 241

The intensity level of an orchestra is 85 dB. A single violin achieves a level of 70 dB. How does the intensity of the sound of the full orchestra compare with that of the violin?

Answer 241

Iorchesta = 31.6Iviolin

Question 242

When a workman strikes a steel pipeline with a hammer, he generates both longitudinal and transverse waves. The two types of reflected waves return 2.4 s apart. How far away is the reflection point? (For steel, vL = 6.2 km/s, vT = 3.2 km/s)

Answer 242

7.9 km