Chapter 5 - Periodic Motion and Waves

Question 1

Equation: wavelength (first harmonic)

Answer 1

λ₁ = 2L/1

Question 2

Equation: frequency of standing waves

Answer 2

f_n = nv/2L

n = # harmonic

Question 3

Equation: frequency of standing waves in relation to the fundamental frequency

Answer 3

f_n = nf₁

Question 4

What is a standing wave?

Answer 4

It appears to have no propagation velocity and is the result of the interference of two waves traveling in opposite directions

Question 5

Does waves transfer matter or energy?

Answer 5

just energy

Question 6

Equation: wavelength (second harmonic)

Answer 6

λ₂ = 2L/2

Question 7

What two forces act on a simple pendulum?

Answer 7

weight (mg) and tension (perpendicular to the arc)

Question 8

What is the frequency of a wave?

Answer 8

the number of vibrations of the wave per unit time

Question 9

What is simple harmonic motion?

Answer 9

vibrating motion, as an object moves back and forth

Question 10

Equation: restoring force of pendulum

Answer 10

F_restoring = -mgsinθ

Question 11

What is meant by an object said to be elastic?

Answer 11

The object experiences a deformation while being compressed or stretched.

Question 12

Equation: frequency of a spring system

Answer 12

f = 1/2π √(k/m)

Question 13

Equation: frequency of a pendulum

Answer 13

f = 1/2π √(g/L)

Question 14

Define amplitude of motion (A)

Answer 14

the magnitude of displacement of the object from equilibrium

Question 15

Equation: wave velocity in regards to frequency

Answer 15

v = λf

Question 16

Equation: frequency of first harmonic (fundamental frequency)

Answer 16

f₁ = v/2L

Question 17

In a standing wave, what are nodes

Answer 17

areas of no vibration

Question 18

What is the amplitude of a wave?

Answer 18

magnitude of maximum displacement of a wave from its point of equilibium

Question 19

Diagram of standing wave: first harmonic

Answer 19

Question 20

If a spring is let go, where is kinetic energy the smallest (0)?

Answer 20

at the greatest magnitude of amplitude (greatest compression and greatest stretch)

Question 21

What is a beat?

Answer 21

when two waves of differing wavelengths interfere with each other

Question 22

What is meant by the negative sign in Hooke’s Law?

Answer 22

The spring experiences a restoring force that acts in the opposite direction of the spring’s displacement.

Question 23

Equation: wavelength (third harmonic)

Answer 23

λ₃ = 2L/3

Question 24

What is the principle of superposition? When does it not hold?

Answer 24

It two or more waves passing through the same medium meet at a particular point in that medium, the net displacement by those waves is the addition of the individual displacements by the waves as if they were traveling through the medium alone. The only time it does not hold is when the waves’ amplitudes are large enough that combined, they change physical properties of the surrounding medium.

Question 25

Define period of motion (T)

Answer 25

the time required to complete one full cycle of motion (time/vibration)

Question 26

What is dampened harmonic oscillation?

Answer 26

The system loses energy as it vibrates, but retains a constant period (because amplitude and speed both decrease).

Question 27

Equation: potential energy of a spring

Answer 27

U_spring = 1/2kx²

Question 28

If a spring is let go, where is kinetic energy the greatest?

Answer 28

at the line of equilibrium

Question 29

What are the units of the spring constant?

Answer 29

N/m

Question 30

If you let a pendulum go, where is the kinetic energy the smallest (0)?

Answer 30

at the greatest magnitude of amplitude

Question 31

Describe transverse waves

Answer 31

They cause vibrations perpendicular to the direction of wave propagation

Question 32

Equation: period of first harmonic

Answer 32

T₁ = 2L/v

Question 33

If you let a pendulum go, where is the kinetic energy the greatest?

Answer 33

at the bottom of the arc, equilibrium (the nadir of the path)

Question 34

Equation: potential energy of a pendulum

Answer 34

U_pendulum = -mgL (1-cosθ)

Question 35

What is wavelength of a wave (λ)?

Answer 35

the distance between two identical points (crest-crest or trough-trough) of disturbance in a wave

Question 36

Equation: frequency in terms of period

Answer 36

f = 1/T

Question 37

Diagram of standing wave: second harmonic

Answer 37

Question 38

What is the speed of a wave?

Answer 38

how far the wave travels per unit time

Question 39

In a standing wave, what are antinodes?

Answer 39

the areas of greatest amplitude (between nodes)

Question 40

What is destructive wave interference?

Answer 40

superposition of two waves that are out of phase If they are of equal amplitude, they will lead to no amplitude, but continue as normal after they have passed each other.

Question 41

Equation: Average force needed to compress a spring

Answer 41

-kx/2

Question 42

Equation: Hooke's Law of force needed to a displace a spring

Answer 42

F = -kx

Question 43

What is resonance?

Answer 43

amplitude/energy of a system may increase if there is a supplied vibrating force that has a frequency which is the same as the natural frequency of the system (pushing a swing at the right time, a singer shattering a glass, NMR)

Question 44

Equation: period of a pendulum

Answer 44

T = 2π √(L/g)

Question 45

Equation: wavelength of standing waves

Answer 45

λ_n = 2L/n n = # harmonic

Question 46

Define frequency of motion (f or ν)

Answer 46

the number of vibrations that occur during a specified amount of time (Hz, vibrations/second)

Question 47

Describe longitudinal waves

Answer 47

They cause vibrations parallel to the direction of wave propagation.

Question 48

Equation: beat frequency

Answer 48

f_beat = l f₂-f₁ l

Question 49

Equation: period of a spring system

Answer 49

T = 2π √(m/k)

Question 50

Which type of standing wave has the longest possible wavelength?

Answer 50

first harmonic

Question 51

What is constructive wave interference?

Answer 51

superposition of waves that are in-phase If they are of equal wavelength, they will create an amplitude twice as high, but continue as normal after they have passed each other.

Question 52

Equation: transverse wave velocity along a string

Answer 52

v = √(T/μ) T = tension in string μ = mass per unit length

Question 53

Equation: wave velocity in regards to period

Answer 53

v = λ/T