green chaddi Flashcards
1
Q
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
A
c. −19k
2
Q
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
A
d. −7j
3
Q
. 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
A
a. (1k )N⋅m
4
Q
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
A
b. 5.0 × 10^6
5
Q
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.
A
a. 50.
6
Q
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
A
a. −30k
7
Q
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
A
a. 0k
8
Q
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
A
e. 21k
9
Q
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
A
d. 20
10
Q
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
A
a. (2/3)g
11
Q
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
A
c. (1/8)g
12
Q
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
A
d. 60
13
Q
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
A
a. m2 gl3 sin4 θ/cos θ
14
Q
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
A
c. 12
15
Q
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
A
d. mvL/2
16
Q
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
A
d. 4.2
17
Q
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
A
b. 3
18
Q
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
A
d. 7.1
19
Q
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
A
a. (5/7)g sin θ
20
Q
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
A
c. (2/3)g sin θ
21
Q
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
A
b. (1/2)g sin θ
22
Q
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
A
a. solid sphere
23
Q
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
A
a. conservation of angular momentum
24
Q
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
A
d. A* vector v pointing to the corner
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.
c. into the page.
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.
c. m2 will stop first because the torque on it is greater.
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.
e. by any force not pointing directly toward or away from the axis of rotation.
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?
a. cylinder with F pointing STRAIGHT to the right
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?
v = 4 m/sr = 2 m M = 20 kg
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?
v = 4 m/sr = 2 m M = 20 kg
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?
Ruler with dot on 2.0
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
d. 4/3 F/M
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
a. 3 kgm^2/s
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.
e. proportional to the speed of the blocks.
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.
b. proportional to the speed of the blocks.
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.
e. cannot be changed except by friction at the point of contact.
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.
d. all of the above are conserved.
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.
e. only momentum and angular momentum are conserved.
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.
b. is the same as the original angular momentum of the station.
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.
b. counterclockwise
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
b. −72k
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)
e. both (a) and (b)
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?
910 m/s
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.
2.89 * 10^34 kgm^2/s
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?
1.65 s
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?
12.4 cm
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
e. y = −0.05 cos 9.9t
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
b. 49
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
a. 7π/3
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
b. −7.9
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
b. 0.25
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
a. 4 times as large
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
d. 1.9
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
c. 4
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
a. 10 s
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
d. 2.3
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
a. 39
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
d. 4.1
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
b. 2.1
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
c. 1.5
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
b. 4
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)
b. −k2x2.
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
a. hoop, cylinder, sphere
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
e. ω1 = ω2 = ω3
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.
c. The rate of change of momentum has its greatest magnitude at A and B.
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.
d. All of the above are correct.
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
e. A and E
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
c. C
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
d. D
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
b. B
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.
b. 0.707 Hz.
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
c. 9.57
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.
a. 84.4 min.
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.
b. 3.07.
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.
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.
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.
e. Neither, because cos(θ + 2π) = cosθ.
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.
d. the projection along the diameter of centripetal acceleration of the particle on the circle.
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.
a. ω < ω0.
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.
c. T > T0.
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.
b. increase the amplitude by sqrt2.
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
c. 6.07 cm
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
d. 32 N/m
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
b. length = 2L, mass = M/2, and maximum angular displacement = 1 degree
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?
2.23 m/s
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.
9.97 cm
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?
600 N/m, 48 J
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.
1.4 m
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?
22 m/s, 14500 N
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
d. 6 × 10^14 Hz
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
c. 15 cm
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
c. 5.5 mm
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
b. 16 m/s
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
c. 675 km
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
b. 520 m/s
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
b. 122 m/s
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
a. 250 Hz
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
c. 0.051 kg
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
c. 200/π Hz
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
a. π/15 m
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
b. 40/3 m/s
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
d. 400 rad/s
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
a. 30 rad/m
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
b. 2.13 W
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)]
a. y = 0.02 sin [880π(x/330 − t)]
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
c. 4 m
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
a. 20 m
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
a. 20 m
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
b. 0.6π m/s
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
b. (cos kx) (sin ωt)
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
b. 8.0 s
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
d. 2.2 W
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.
c. increase the tension on the hose and shake the end fewer times per second.
113
Refer to Exhibit 16-1. Which of the graphs below shows a wave where the amplitude and the frequency are doubled?
Graph with 7 nodes
114
Refer to Exhibit 16-1. Which of the graphs below shows a wave where the amplitude and frequency are each reduced in half?
Graph with 2 nodes (the smaller one)
115
Refer to Exhibit 16-2. Which of the graphs below shows a wave where the frequency and wave velocity are both doubled?
Graph with 4 nodes (the smaller one)
116
Refer to Exhibit 16-2. Which of the graphs below shows a wave where the frequency and wave velocity are both doubled?
Graph with 2 nodes
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.
e. do (a) or (b) above, preferably both.
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.
a. Ariel, because x2 – 6.0xt + 9t2 = (x – 3.0t)2.
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
b. 1/4
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.
d. do any one of the above
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.
e. v2 should be replaced by 1/v^2.
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
b. IV = II, I, III
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
a. IV, II, I, III
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
e. I = III, II, IV
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.
e. a greater distance up, but take the same time.
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.
b. the same distance up as before, but take a longer time.
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.
d. a greater distance up, but take a longer time.
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.
d. The P wave is longitudinal and the S wave is transverse.
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
b. 2 m/s in the −x direction
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)
b. y = Acos(kx-wt)
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)
d. v = -wAcos(kx-wt)
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?
1.0 m/s
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?
5.7 mm
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.
219 N
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
d. 2.41 × 10^9
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
b. 4.3
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
c. 2.70 × 10^3
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
d. 15
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
c. 2.7 × 10−2
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
b. 3.7 × 10^−10
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
b. 477
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
d. 1.01
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
c. 484
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
b. 1.8 × 10−7
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
c. 92
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
d. 1 000
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
c. 2
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
d. 10^10
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
a. 7.96 × 10^−2
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
d. 109
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
d. 552
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
c. 105
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
b. 636
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
d. 396
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
c. 240
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
b. 516
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
d. 1/r1/2
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.
c. molecular displacements are parallel to the wave velocity.
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.
b. wave crests are closer together by the distance the car travels in one period.
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.
c. run away from her at the same speed.
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.
c. reduce the amplitude by a factor of 2 and increase your distance from the speaker by a factor of 3.
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.
c. increase in frequency.
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.
b. stay at the same frequency.
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
c. 0.002 cm/r
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.
a. 0.25 m.
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.
c. 1 360.
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.
c. 340.
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
a. 1/36
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
c. loudness
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.
d. the observer and source are moving away from each other.
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
d. 3.2 m
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
b. 48
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
c. 1 m
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
d. 1
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
a. 90
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
d. 0.25
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
c. 0
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
d. 2.25
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
a. 3.14 m
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
b. 1 Hz
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
a. 0.75
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
d. 1
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
b. 400
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
c. 158 Hz
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
c. 160 Hz
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
c. 86
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
b. 86
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
c. 344
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
d. 172
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)
b. 2
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
a. 269 Hz
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
c. 3 rad/s
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
b. 183 Hz
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
c. 110 Hz, 330 Hz, 550 Hz
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
c. 2.00, 1.00, 0.500
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
d. x = 0.75 m, 1.25 m
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.
d. fn,B = 2fn,A.
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.
d. beats at a beat frequency of 6 Hz in a 153 Hz tone.
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.
c. pi/4 rad.
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.
d. 4 m.
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.
a. 85 Hz.
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.
b. λ/2.
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
d. 0.89 m
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
d. 0.89 m
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.
e. 382 Hz.
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
c. π
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).
e. given by (a) or (b) above, but not by (c).
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
c. A1 + A2.
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).
e. Only the wavelengths listed in (a) and (b).
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.
c. The wavelength of the waves on the string.
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.
d. 1 320, 2 640 and 3 960 Hz.
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.
e. They have no overtones in common.
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.
e. After the first overtone of each pipe, every third overtone of the first pipe matches every fourth overtone of the second pipe.
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
a. 0.
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
e. 2π
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.
c. 3π.
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
a. ω/k
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.
c. with a high Young's modulus and a low density.
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
b. 15
220
The figure below shows the positions of particles in a longitudinal standing wave. One quarter period later the particle distribution is shown in
longest consecutive chain of dots
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
a. 3
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
b. 45 N
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
b. 95 Hz
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.
d. in all of the above.
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?
square 3 cm long
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
small speed bump and large speed bump
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
small divot and then large speed bump
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?
150 Hz
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.
100 Hz, 200 Hz, 300 Hz
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)?
824 N
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
c. 2.24
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.
b. 1.99 × 10^−2.
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.
d. 4
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.
d. much longer than the length of either a man's or a woman's lips.
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).
b. It increases.
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.
b. 640 m/s
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
d. 1 000 Hz
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.)
41.2 kHz
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.
19.7 km
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.
10000 Hz, 3333 Hz
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?
Iorchesta = 31.6Iviolin
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)
7.9 km
