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Physics 1B > Ch 15: Waves > Flashcards

Ch 15: Waves Flashcards

1
Q

mechanical wave

A

disturbance that travels through a medium

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2
Q

transverse wave

A

displacements of medium are perpendicular to direction of travel of the wave

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3
Q

longitudinal wave

A

motions of the particles of the medium are back and forth along the same direction that the wave travels

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4
Q

wave speed

A

speed at which the wave propagates through the medium

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5
Q

T/F: Wave speed is not the same as the speed with which the individual particles move.

A

TRUE TRUE

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6
Q

T/F: The medium itself does travel through space when there is a wave going through it.

A

FALSE

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7
Q

Waves transport _____, not _____, from one region to another.

A

energy; matter

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8
Q

On a periodic transverse wave, each particle undergoes periodic motion with _____.

A

the same frequency, and wave speed is constant.

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9
Q

wave function for a sinusoidal wave moving in the +x-direction

A

y(x,t) =Acos(kx - ωt), where y is the displacement of a particle at time t and position x

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10
Q

wave function for a sinusoidal wave moving in the -x-direction

A

y(x,t) =Acos(kx + ωt)

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11
Q

compression

A

region of increased density

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12
Q

rarefaction

A

region of reduced density

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13
Q

wavelength of a periodic longitudinal wave

A

distance from compression to compression or rarefaction to rarefaction

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14
Q

wave number

A

k = 2π/λ

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15
Q

At time t, one point has maximum positive displacement while another point has maximum negative displacement- these two are a ______ cycle ______phase

A

half; out of

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16
Q

In the wave function, when y=A, what is the motion of the particle?

A

It is instantaneously at rest

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17
Q

wave speed for periodic transverse wave

A

v = λ/T = λf; generally determined by the mechanical properties of the medium and is constant (so increasing f causes λ to decrease and waves of all frequencies propagate with the same wave speed)

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18
Q

For a periodic wave, ω =

A

vk

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19
Q

If you use the wave equation to plot y as a function of x for time t, the curve shows _____.

A

the shape of the string at t

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20
Q

If you use the wave equation to plot y as a function of t for position x, the curve shows _____.

A

the displacement y of a particle at that coordinate as a function of time

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21
Q

phase

A

(kx ± ωt); plays the role of an angular quantity; determines what part of the sinusoidal cycle is occuring

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22
Q

What are the possible values of the phase for a crest (y = A)?

A

0, 2π, 4π, …

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23
Q

What are the possible values of the phase for a trough (y = -A)?

A

π, 3π, 5π, …

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24
Q

If you take the derivative of the phase, what do you get?

A

dx/dt = ω/k = v; aka phase velocity or speed

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25
Q

Given y(x,t) = Acos[2π/λ(x−vt)], what is an expression for the transverse velocity v_y at a fixed point x?

A

Take the partial derivative with respect to t:

v_y = (2πvA)/λ sin[2π/λ(x−vt)] or ωAsin (kx - ωt)

26
Q

Given v_y = (2πvA)/λ sin[2π/λ(x−vt)], what is the maximum transverse speed of a particle on a string?

A

The speed is maximized when the sin term = 1, so v_max = (2πvA/λ), or ωA

27
Q

What is the transverse acceleration (a_y) of a particle on a string?

A

Take the second partial derivative of y(x,t) with respect to t:
-ω²Acos(kx-ωt), which is simply -ω²y(x,t)

28
Q

If you take the first partial derivative of the wave equation with respect to x, what do you get?

A

the slope of the string at point x and time t, -kA sin(kx-ωt)

29
Q

If you take the second partial derivative of the wave equation with respect to x, what do you get?

A

the curvature of the string at point x and time t, -k²Acos(kx-ωt), which is simply -k²y(x,t)

30
Q

What are the physical quantities that determine the speed of transverse waves on a string?

A

tension, mass per unit length (aka linear mass density)

31
Q

Increasing the tension in a string increases the restoring forces that tend to straighten out the string when it is disturbed, thus increasing the _____.

A

wave speed

32
Q

Increasing the mass of a string decreases the _____.

A

wave speed

33
Q

The momentum of the moving portion of a string increases with time because _____.

A

more mass is brought into motion- the wave propagates at a constant speed v and so the increase in momentum is not due to an increasing v

34
Q

What is the equation for the speed of a transverse wave on a string?

A

v = √(T/μ), where T is the tension and μ is the mass per unit length

35
Q

What is the general form for wave speed?

A

v = √(restoring force returning the system to equilibrium/inertia resisting the return to equilibrium)

36
Q

What is the power at a point on a sting?

A

the transverse force multiplied by the transverse velocity; the instantaneous rate at which energy is transferred along the string;

P(x,t)= F_y(x,t) v_y(x,t), where F_y is equal to the negative slope of the string (negative first partial derivative of the wave function with respect to x) at that point times the force, and v_y is equal to the first partial derivative of the wave function with respect to t

37
Q

What is an alternate form of the power expression (using the wave function form)?

A

P(x,t) = √(μF) ω²A²sin²(kx-ωt)

38
Q

What is the maximum instantaneous power, P_max?

A

P_max = √(μF) ω²A²

39
Q

What is average power, P_av?

A

P_av = ½ √(μF) ω²A², since the average value of the sin² function is ½

40
Q

intensity

A

average power per unit area, usually measured in watt per square meter; if the waves spread out equally in all directions, the intensity at distance r is:

I= P/(4πr²)

41
Q

What is the inverse square law for intensity?

A

I_1/I_2 = r²_2/r²_1 if no energy is absorbed between the two spheres, making the power P the same for both

42
Q

How do you find the frequency from the wave equation y(x,t) =Acos(kx - ωt)?

A

ω is equal to 2πf, so f =ω/2π

43
Q

How do you find the wavelength from the wave equation y(x,t) =Acos(kx - ωt)?

A

k is equal to 2π/λ, so λ=2π/k

44
Q

What are the units for μ?

A

kg/m

45
Q

What are the units for T?

A

seconds/cycle

46
Q

What are the units for f?

A

cycles/second

47
Q

What are the units for ω?

A

rad/s

48
Q

What are the units for intensity?

A

W/m²

49
Q

How do you find the tension in a rope from the wave equation y(x,t) =Acos(kx - ωt)?

A

You find f by using ω=2πf, λ by using k=2π/λ, and v by using v=λf. Then you use the equation v = √(T/μ)

50
Q

When there are two speakers out of phase facing each other, at what points will the sound be the loudest?

A

at the nodes

51
Q

When a wave reflects from a fixed end, the pulse _____. Why?

A

inverts as it reflects; if a string exerts an upward force on a wall, the wall exerts a downward reaction force on the string, and so when the string is reflected, it travels on the opposite side of the string

52
Q

When a wave reflects from a free end, the pulse _____. Why?

A

reflects without inverting; if a string reaches a free end, the free end exerts no transverse force on the string, and so the wave is reflected on the same side of the string

53
Q

When a wave strikes the boundaries of its medium, all or part of the wave is _____.

A

reflected

54
Q

interference

A

overlapping of waves

55
Q

principle of linear superposition of waves

A

when 2 or more waves overlap, the total displacement is the sum of the displacements of the individual waves (add the two wave functions); y(x,t) = y_1(x,t) + y_2(x,t)

56
Q

node

A

on a string, this is a point at which the string never moves

57
Q

antinode

A

on a string, this is a point halfway between nodes and is where the amplitude of the string’s motion is the greatest

58
Q

What is the distance between nodes or the distance between antinodes

A

½λ

59
Q

What is the wave function for a standing wave on a string?

A

y(x,t) = (A_sw sin kx)sin ωt, where A_sw = 2A

60
Q

Where are the nodes of a standing wave on a string, with fixed end at x=0?

A

0, λ/2, λ, 3λ/2, …

61
Q

Unlike a traveling wave, a standing wave _____.

A

does not transfer energy from one end to the other

Physics 1B (7 decks)

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