Question 1

As one approaches the bottom of a body of water, the circles shown in figure Q1.3 for water waves moving along the water's surface become increasingly vertically flattened ellipses. This means that the waves near the body's bottom are more (A) transverse or (B) longitudinal than those near the surface?

A) Transverse
B) Longitudinal

Accepted Answer

B

Question 2

Imagine a series of mutually repelling ring magnets strung along a nearly frictionless horizontal rigid rod. If one jostles a magnet near one end of the rod, it can cause a wave of disturbance to move down the rod through the other magnets. Will this be a (A) transverse or (B) longitudinal wave?
A) Transverse wave
B) Longitudinal wave

Accepted Answer

The disturbance moves along the direction of the rod, causing the magnets to move back and forth in the same direction as the wave's propagation. This is characteristic of a longitudinal wave, where the displacement of the medium is parallel to the direction of the wave's travel.

Question 3

As a sinusoidal wave's wavenumber increases, the wave's wavelength (in a non-dispersive medium)
A) Increases.
B) Decreases.
C) Does not change.

Accepted Answer

The wavenumber is inversely proportional to the wavelength, so as the wavenumber increases, the wavelength decreases.

Question 4

A sinusoidal wave's angular frequency is (A) larger, (B) smaller, or (C) the same as its frequency in cycles/s.
A) Large
B) Smaller
C) The same as its frequency in cycles/s.

Accepted Answer

Angular frequency is larger than frequency in cycles/s because it is measured in radians per second, and there are $2\pi$ radians in one cycle.

Question 5

Equation $|\vec{v}|=\frac{\omega}{k}=\frac{\lambda}{T}=\lambda f$ implies that a sinusoidal wave's phase speed depends on its wavelength.

Accepted Answer

The answer of Equation $|\vec{v}|=\frac{\omega}{k}=\frac{\lambda}{T}=\lambda f$ implies that a sinusoidal...

Question 6

Consider wiggle formula $w(t, x)=f(\mathrm{bx}+\mathrm{ct})$ for a transverse wave, where $b$ and $c$ are constants and $f()$ is some arbitrary function. Is this a traveling wave model? If so, in what direction does it travel?
A) In the $+x$ direction.
B) In the $-x$ direction.
C) The wave does not move.
D) In the $y$ or $z$ direction because the wave is transverse.

Accepted Answer

The wave travels in the $-x$ direction because the argument of the function $f(\mathrm{bx}+\mathrm{ct})$ increases with time $t$ for a fixed position $x$, indicating that the wave peaks move in the negative $x$ direction as time progresses.

Question 7

In a specific non-dispersive medium, a sinusoidal wave's angular frequency is proportional to its wavenumber.

Accepted Answer

In a non-dispersive medium, the phase velocity of a wave is constant, meaning that the angular frequency (ω) is directly proportional to its wavenumber (k), following the relation ω = vk, where v is the phase velocity.

Question 8

In a specific non-dispersive medium, a sinusoidal wave's period is proportional to its wavelength.

Accepted Answer

In a non-dispersive medium, the wave speed is constant, so the period is proportional to the wavelength as both are related by the wave speed.

Question 9

If one sound is $20 \mathrm{~dB}$ louder than another sound, its intensity is
A) 2 times greater.
B) 20 times greater.
C) 100 times greater.
D) 200 times greater.
E) We need to know the actual sound level: $30 \mathrm{db}$ to $50 \mathrm{db}$ represents a different factor of intensity increase than 60 $\mathrm{db}$ to $80 \mathrm{db}$ (for example).

Accepted Answer

The decibel (dB) scale is logarithmic, where a 10 dB increase represents a tenfold increase in intensity. Therefore, a 20 dB increase indicates a 100-fold (10^2) increase in intensity.

Question 10

A linear traveling wave can be partially reflected when it encounters another linear traveling wave.

Accepted Answer

A linear traveling wave can be partially reflected when it encounters a change in the medium through which it is traveling, not merely by encountering another linear traveling wave. Reflection occurs at boundaries where the properties of the medium change, not due to the interaction with another wave in the same medium.

Question 11

A sound wave traveling in air hits the surface of a body of water. Is the reflected wave (A) inverted or (B) upright? (Make a guess.)
A) Inverted
B) Upright

Accepted Answer

The answer of A sound wave traveling in air hits...

Question 12

A sound wave traveling in air hits the surface of a body of water. The reflection will be total.

Accepted Answer

When a sound wave traveling in air hits the surface of a body of water, some of the sound is reflected back into the air, but not all of it. Some of the sound energy will also be transmitted into the water, so the reflection is not total.

Question 13

Imagine that the wave shown below moves right along a stretched string. It meets and passes through one of the left-going waves provided in the choices. For which choice is there an instant where the string is flat?

A) A
B) B
C) C
D) D
E) None of the above

Accepted Answer

The answer of Imagine that the wave shown below moves...

Question 14

Consider the right-going wave and the possible left-going waves displayed in problem Q2T.3. For which of the choices will there be an instant where the combined wave is a rectangular wave as shown below?

A) A
B) B
C) C
D) D
E) None of the above

Accepted Answer

The answer of Consider the right-going wave and the possible...

Question 15

Suppose we create a traveling compression wave in a spring that has one end fixed. When the wave reflects from the fixed end, it will be inverted (that is, compression will become rarefaction and vice versa).

Accepted Answer

The answer of Suppose we create a traveling compression wave...

Question 16

Suppose you are near one end of a 150-m-long cylindrical tunnel open to the air on both ends. If you give a shout, you might hear an echo.

Accepted Answer

Sound can reflect off surfaces such as the walls of a tunnel. If the tunnel is long enough, the sound of your shout can travel to the other end, reflect off the wall, and travel back to you as an echo.

Question 17

If you face a cliff and give a shout, you will hear an echo. Are the sound waves of the echo inverted (A) or upright (B) compared to the waves of your original shout?
A) Inverted
B) Upright

Accepted Answer

The sound waves of the echo are upright compared to the waves of your original shout. When sound waves bounce off a surface like a cliff and return as an echo, they maintain the same wave orientation as the original sound.

Question 18

The frequencies of the normal modes of a string that is free at both ends are the same as those of a string that is fixed at both ends.

Accepted Answer

The boundary conditions for both cases allow for standing waves with nodes at both ends, resulting in the same set of harmonic frequencies.

Question 19

A sinusoidal standing sound wave inside a tube that is open at both ends must fit between the tube's ends
A) An integer number of wavelengths.
B) An integer number of half-wavelengths.
C) An integer number of quarter-wavelengths
D) An odd-integer number of half-wavelengths.
E) An odd-integer number of quarter-wavelengths.

Accepted Answer

For a tube open at both ends, the sound wave must fit such that there are antinodes at both ends. This condition is met when the tube length is an integer number of half-wavelengths, allowing the wave to fit perfectly within the tube with antinodes at the openings.

Question 20

The normal mode of a resonating system is sinusoidally disturbed at a frequency $f$. Assume that $\gamma<<f_{0}$, where $f_{0}$ is the normal mode's natural frequency.
-(a) What is the amplitude of the normal mode's oscillation compared to its amplitude $A_{0}$ in the limit that the disturbance frequency goes to zero if $f$ is about $1.4 f_{0}$ ?
A) Roughly zero
B) Roughly $A_{0} / 30$
C) Roughly $A_{0} / 1.4$
D) Roughly $A_{0}$
E) Roughly $1.4 \mathrm{~A}_{0}$
F) Roughly $30 A_{0}$
G) Other (specify)

Accepted Answer

The answer of The normal mode of a resonating system...

Quiz 5: Matter Behaves Like Waves Quantum Physics

Imagine a series of mutually repelling ring magnets strung along a nearly frictionless horizontal rigid rod. If one jostles a magnet near one end of the rod, it can cause a wave of disturbance to move down the rod through the other magnets. Will this be a (A) transverse or (B) longitudinal wave?

As a sinusoidal wave's wavenumber increases, the wave's wavelength (in a non-dispersive medium)

A sinusoidal wave's angular frequency is (A) larger, (B) smaller, or (C) the same as its frequency in cycles/s.

Equation $|\vec{v}|=\frac{\omega}{k}=\frac{\lambda}{T}=\lambda f$ implies that a sinusoidal wave's phase speed depends on its wavelength.

Consider wiggle formula $w(t, x) =f(\mathrm{bx}+\mathrm{ct})$ for a transverse wave, where $b$ and $c$ are constants and $f()$ is some arbitrary function. Is this a traveling wave model? If so, in what direction does it travel?

In a specific non-dispersive medium, a sinusoidal wave's angular frequency is proportional to its wavenumber.

In a specific non-dispersive medium, a sinusoidal wave's period is proportional to its wavelength.

If one sound is $20 \mathrm{~dB}$ louder than another sound, its intensity is

A linear traveling wave can be partially reflected when it encounters another linear traveling wave.

A sound wave traveling in air hits the surface of a body of water. Is the reflected wave (A) inverted or (B) upright? (Make a guess.)

A sound wave traveling in air hits the surface of a body of water. The reflection will be total.

Imagine that the wave shown below moves right along a stretched string. It meets and passes through one of the left-going waves provided in the choices. For which choice is there an instant where the string is flat?

Consider the right-going wave and the possible left-going waves displayed in problem Q2T.3. For which of the choices will there be an instant where the combined wave is a rectangular wave as shown below?

Suppose we create a traveling compression wave in a spring that has one end fixed. When the wave reflects from the fixed end, it will be inverted (that is, compression will become rarefaction and vice versa).

Suppose you are near one end of a 150-m-long cylindrical tunnel open to the air on both ends. If you give a shout, you might hear an echo.

If you face a cliff and give a shout, you will hear an echo. Are the sound waves of the echo inverted (A) or upright (B) compared to the waves of your original shout?

The frequencies of the normal modes of a string that is free at both ends are the same as those of a string that is fixed at both ends.

A sinusoidal standing sound wave inside a tube that is open at both ends must fit between the tube's ends

Quiz 5: Matter Behaves Like Waves Quantum Physics

Imagine a series of mutually repelling ring magnets strung along a nearly frictionless horizontal rigid rod. If one jostles a magnet near one end of the rod, it can cause a wave of disturbance to move down the rod through the other magnets. Will this be a (A) transverse or (B) longitudinal wave?

As a sinusoidal wave's wavenumber increases, the wave's wavelength (in a non-dispersive medium)

A sinusoidal wave's angular frequency is (A) larger, (B) smaller, or (C) the same as its frequency in cycles/s.

Equation ∣v⃗∣=ωk=λT=λf|\vec{v}|=\frac{\omega}{k}=\frac{\lambda}{T}=\lambda f∣v∣=kω​=Tλ​=λf implies that a sinusoidal wave's phase speed depends on its wavelength.

Consider wiggle formula w(t,x) =f(bx+ct) w(t, x) =f(\mathrm{bx}+\mathrm{ct}) w(t,x) =f(bx+ct) for a transverse wave, where bbb and ccc are constants and f() f() f() is some arbitrary function. Is this a traveling wave model? If so, in what direction does it travel?

In a specific non-dispersive medium, a sinusoidal wave's angular frequency is proportional to its wavenumber.

In a specific non-dispersive medium, a sinusoidal wave's period is proportional to its wavelength.

If one sound is 20 dB20 \mathrm{~dB}20 dB louder than another sound, its intensity is

A linear traveling wave can be partially reflected when it encounters another linear traveling wave.

A sound wave traveling in air hits the surface of a body of water. Is the reflected wave (A) inverted or (B) upright? (Make a guess.)

A sound wave traveling in air hits the surface of a body of water. The reflection will be total.

Imagine that the wave shown below moves right along a stretched string. It meets and passes through one of the left-going waves provided in the choices. For which choice is there an instant where the string is flat?

Consider the right-going wave and the possible left-going waves displayed in problem Q2T.3. For which of the choices will there be an instant where the combined wave is a rectangular wave as shown below?

Suppose we create a traveling compression wave in a spring that has one end fixed. When the wave reflects from the fixed end, it will be inverted (that is, compression will become rarefaction and vice versa).

Suppose you are near one end of a 150-m-long cylindrical tunnel open to the air on both ends. If you give a shout, you might hear an echo.

If you face a cliff and give a shout, you will hear an echo. Are the sound waves of the echo inverted (A) or upright (B) compared to the waves of your original shout?

The frequencies of the normal modes of a string that is free at both ends are the same as those of a string that is fixed at both ends.

A sinusoidal standing sound wave inside a tube that is open at both ends must fit between the tube's ends

Equation $|\vec{v}|=\frac{\omega}{k}=\frac{\lambda}{T}=\lambda f$ implies that a sinusoidal wave's phase speed depends on its wavelength.

Consider wiggle formula $w(t, x) =f(\mathrm{bx}+\mathrm{ct})$ for a transverse wave, where $b$ and $c$ are constants and $f()$ is some arbitrary function. Is this a traveling wave model? If so, in what direction does it travel?

If one sound is $20 \mathrm{~dB}$ louder than another sound, its intensity is