Question 1

The intensity of the waves from a point source at a distance d from the source is I. At what distance from the sources is the intensity equal to 2I?

Accepted Answer

According to the inverse square law, intensity is inversely proportional to the square of the distance from the source. Therefore, if the distance is increased by a factor of √2, the intensity will decrease by a factor of (sqrt(2))^2 = 2. So, the intensity at a distance of d/√2 will be 2I.

Question 2

What is the frequency of the wave shown in the figure?

Accepted Answer

A

Question 3

When a certain string is under tension T, the speed of a wave in the string is v. What will be the speed of a wave in the string if the tension is increased to 2T without changing the mass or length of the string?

Accepted Answer

The speed of a wave in a string is given by v = $\sqrt{\frac{T}{\mu}}$, where T is the tension in the string and $\mu$ is the linear mass density of the string (mass per unit length). Since the mass and length of the string are not changing, $\mu$ is constant. When the tension is increased to 2T, the new speed of the wave is v' = $\sqrt{\frac{2T}{\mu}}$. Taking the ratio of v' to v, we get v'/v = $\sqrt{\frac{2T}{T}}$ = $\sqrt{2}$. Therefore, the speed of the wave has increased by a factor of $\sqrt{2}$, so the answer is C.

Question 4

As you are moving very quickly toward a speaker emitting a pure tone, which characteristics of the sound get larger? (There may be more than one correct choice.)

Accepted Answer

When moving quickly toward a speaker, the frequency of the sound increases due to the Doppler effect, making the pitch higher. This perceived increase in frequency can also make the sound seem louder, hence affecting the loudness. The amplitude, wavelength, and period of the sound wave itself do not inherently change just by the listener moving towards the source; these changes are related to the source's output and the medium through which the sound travels.

Question 5

In many cartoon shows, a character runs off a cliff, realizes his predicament, and lets out a scream. He continues to scream as he falls. If the physical situation is portrayed correctly, from the vantage point of an observer at the foot of the cliff, the pitch of the scream as he falls should be

Accepted Answer

As the character falls, he will be accelerating downwards due to gravity. This means his velocity will be increasing, which will in turn cause the pitch of his scream to increase as well. Therefore, the correct choice is B: higher than the original pitch and increasing as he falls.

Question 6

Seven seconds after a brilliant flash of lightning, thunder shakes the house. Approximately how far was the lightning strike from the house?

Accepted Answer

Since sound travels at a speed of approximately 343 meters per second, we can estimate the distance of the lightning strike by multiplying the time interval between lightning and thunder by the speed of sound. In this case, 7 seconds times 343 meters per second gives us a distance of approximately 2 kilometers. Therefore, the answer is C, about two kilometers away.

Question 7

Four waves are described by the following equations, where distances are measured in meters and times in seconds. 
I. y = 0.12 cos(3x - 21t)
II. y = 0.15 sin(6x + 42t)
III. y = 0.13 cos(6x + 21t)
IV. y = -0.23 sin(3x - 42t)
Which of these waves have the same period?

Accepted Answer

The period of a wave is determined by the coefficient of $t$ in the argument of the sine or cosine function, which is related to the angular frequency $\omega$. Waves I and III have the same absolute value for the coefficient of $t$ (21), indicating they have the same period. Similarly, waves II and IV have the same absolute value for the coefficient of $t$ (42), indicating they also share the same period.

Question 8

Why does the intensity of waves from a small source decrease with the square of the distance from the source?

Accepted Answer

The intensity of waves from a small source decreases with the square of the distance from the source due to wave spreading. As waves move away from the source they spread out, occupying a larger area. This means that the same amount of energy is distributed over a larger area, resulting in a decrease in intensity that is proportional to the square of the distance.

Question 9

What characteristics of a sound wave are related to the "pitch" of a musical note? (There could be more than one correct choice.)

Accepted Answer

The answer of What characteristics of a sound wave are...

Question 10

You double your distance from a sound source that is radiating equally in all directions. What happens to the intensity of the sound? It reduces to

Accepted Answer

The intensity of sound at a point is directly proportional to the square of the distance from the source. Therefore, if the distance is doubled, the intensity reduces to one-fourth its original value.

Question 11

The intensity of the waves from a point source at a distance d from the source is I. What is the intensity at a distance 2d from the source?

Accepted Answer

The intensity of waves from a point source decreases with the square of the distance from the source. So, if the distance from the source is doubled, the intensity would decrease by a factor of (2)^2 = 4. Therefore, the intensity at a distance 2d from the source would be I/4.

Question 12

A string of length L is under tension, and the speed of a wave in the string is v. What will be the speed of a wave in the string if the length is increased to 2L but with no change in the mass or tension?

Accepted Answer

The speed of a wave in a string is given by:$$v = \sqrt{\frac{T}{\mu}}$$where T is the tension in the string and $\mu$ is the linear mass density of the string. If the length of the string is increased to 2L, the linear mass density will be reduced to $\mu/2$. Therefore, the speed of the wave will become:$$v' = \sqrt{\frac{T}{\mu/2}} = \sqrt{2}v$$

Question 13

In many cartoon shows, a character runs off a cliff, realizes his predicament, and lets out a scream. He continues to scream as he falls. If the physical situation is portrayed correctly, from the vantage point of an observer at the top of the cliff leaning over the edge, the pitch of the scream as he falls should be

Accepted Answer

As the character falls, the distance between them and the observer at the top of the cliff increases, causing a decrease in the pitch (frequency) of the sound. Therefore, the scream should be lower in pitch and decreasing as the character falls.

Question 14

Which one of the curves shown in the figure best represents the variation of wave speed v as a function of tension for transverse waves on a stretched string?

Accepted Answer

The answer of Which one of the curves shown in...

Question 15

What is the wavelength of the wave shown in the figure?

Accepted Answer

The answer of What is the wavelength of the wave...

Question 16

Four waves are described by the following equations, where distances are measured in meters and times in seconds. 
I. y = 0.12 cos(3x - 21t)
II. y = 0.15 sin(6x + 42t)
III. y = 0.13 cos(6x + 21t)
IV. y = -0.23 sin(3x - 42t)
Which of these waves have the same speed?

Accepted Answer

The answer of Four waves are described by the following...

Question 17

Suppose that a sound source is emitting waves uniformly in all directions. If you move to a point twice as far away from the source, the frequency of the sound will be

Accepted Answer

The frequency of sound is determined by the source, not by the distance between the source and the observer. Therefore, if you move to a point twice as far away from the source, the frequency of the sound will remain the same.

Question 18

A string of mass m is under tension, and the speed of a wave in the string is v. What will be the speed of a wave in the string if the mass of the string is increased to 2m but with no change in the length or tension?

Accepted Answer

The speed of a wave on a string is given by 
v = √(T/μ)
where T is the tension in the string and μ is the linear mass density (mass per unit length) of the string. Since the length and tension of the string are constant, the speed of the wave is directly proportional to the square root of the linear mass density. When the mass of the string is increased to 2m, the linear mass density doubles (μ → 2μ), so the speed of the wave decreases by a factor of √2 (v → v/√2). Therefore, the correct answer is B.

Question 19

A fisherman fishing from a pier observes that the float on his line bobs up and down, taking 2.4 s to move from its highest point to its lowest point. He also estimates that the distance between adjacent wave crests is 48 m. What is the speed of the waves going past the pier?

Accepted Answer

The time taken for one complete wave to pass a point is known as the period, T. In this case, the period can be calculated as:

T = 2 × 2.4 s = 4.8 s

The frequency of the wave, f, is the inverse of the period:

f = 1/T = 1/4.8 s ≈ 0.208 Hz

The speed of the wave, v, can be calculated as:

v = f × λ = 0.208 Hz × 48 m ≈ 10 m/s

Therefore, the answer is choice C, 10 m/s.

Question 20

Sound A has a high pitch and sound B has a low pitch. Which of the following statements about these two sounds are correct? (There could be more than one correct choice.)

Accepted Answer

B) High-pitched sounds have shorter periods because their waves cycle faster. C) High-pitched sounds have greater frequencies, as pitch directly correlates with frequency.

Quiz 15: Traveling Waves and Sound