Ch 15: Waves

Question 1

mechanical wave

Answer 1

disturbance that travels through a medium

Question 2

transverse wave

Answer 2

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

Question 3

longitudinal wave

Answer 3

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

Question 4

wave speed

Answer 4

speed at which the wave propagates through the medium

Question 5

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

Answer 5

TRUE TRUE

Question 6

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

Answer 6

FALSE

Question 7

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

Answer 7

energy; matter

Question 8

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

Answer 8

the same frequency, and wave speed is constant.

Question 9

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

Answer 9

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

Question 10

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

Answer 10

y(x,t) =Acos(kx + ωt)

Question 11

compression

Answer 11

region of increased density

Question 12

rarefaction

Answer 12

region of reduced density

Question 13

wavelength of a periodic longitudinal wave

Answer 13

distance from compression to compression or rarefaction to rarefaction

Question 14

wave number

Answer 14

k = 2π/λ

Question 15

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

Answer 15

half; out of

Question 16

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

Answer 16

It is instantaneously at rest

Question 17

wave speed for periodic transverse wave

Answer 17

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)

Question 18

For a periodic wave, ω =

Answer 18

vk

Question 19

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

Answer 19

the shape of the string at t

Question 20

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

Answer 20

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

Question 21

phase

Answer 21

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

Question 22

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

Answer 22

0, 2π, 4π, …

Question 23

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

Answer 23

π, 3π, 5π, …

Question 24

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

Answer 24

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

Question 25

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

Answer 25

Take the partial derivative with respect to t: | v_y = (2πvA)/λ sin[2π/λ(x−vt)] or ωAsin (kx - ωt)

Question 26

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

Answer 26

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

Question 27

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

Answer 27

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

Question 28

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

Answer 28

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

Question 29

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

Answer 29

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

Question 30

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

Answer 30

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

Question 31

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

Answer 31

wave speed

Question 32

Increasing the mass of a string decreases the _____.

Answer 32

wave speed

Question 33

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

Answer 33

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

Question 34

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

Answer 34

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

Question 35

What is the general form for wave speed?

Answer 35

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

Question 36

What is the power at a point on a sting?

Answer 36

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

Question 37

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

Answer 37

P(x,t) = √(μF) ω²A²sin²(kx-ωt)

Question 38

What is the maximum instantaneous power, P_max?

Answer 38

P_max = √(μF) ω²A²

Question 39

What is average power, P_av?

Answer 39

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

Question 40

intensity

Answer 40

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)

Question 41

What is the inverse square law for intensity?

Answer 41

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

Question 42

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

Answer 42

ω is equal to 2πf, so f =ω/2π

Question 43

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

Answer 43

k is equal to 2π/λ, so λ=2π/k

Question 44

What are the units for μ?

Answer 44

kg/m

Question 45

What are the units for T?

Answer 45

seconds/cycle

Question 46

What are the units for f?

Answer 46

cycles/second

Question 47

What are the units for ω?

Answer 47

rad/s

Question 48

What are the units for intensity?

Answer 48

W/m²

Question 49

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

Answer 49

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)

Question 50

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

Answer 50

at the nodes

Question 51

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

Answer 51

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

Question 52

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

Answer 52

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

Question 53

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

Answer 53

reflected

Question 54

interference

Answer 54

overlapping of waves

Question 55

principle of linear superposition of waves

Answer 55

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)

Question 56

node

Answer 56

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

Question 57

antinode

Answer 57

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

Question 58

What is the distance between nodes or the distance between antinodes

Answer 58

½λ

Question 59

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

Answer 59

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

Question 60

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

Answer 60

0, λ/2, λ, 3λ/2, ...

Question 61

Unlike a traveling wave, a standing wave _____.

Answer 61

does not transfer energy from one end to the other