Question 1

The figure represents a wire of length L, fixed at both ends, vibrating in several harmonics. The 3rd harmonic is shown in
A) 1).
B) 2).
C) 3).
D) 4).
E) 5).

Accepted Answer

The answer of  The figure represents a wire of...

Question 2

A pulse moves in a string toward a free end a ring on a post) as indicated in the sketch. On reflection, the pulse would most nearly be represented by
A) 1.
B) 2.
C) 3.
D) 4.
E) 5.

Accepted Answer

The answer of  A pulse moves in a string...

Question 3

From the figure above, you can conclude that
A) the medium to the left of the boundary is denser than the medium to the right.
B) the medium to the right of the boundary is denser than the medium to the left.
C) the pulse is initially traveling from right to left.
D) the wave has lost energy as a result.
E) None of these is correct.

Accepted Answer

The answer of  From the figure above, you can...

Question 4

The figure shows two waves traveling in the positive-x direction. The amplitude of the resultant wave is closest to
A) 2.0 mm.
B) 1.8 mm.
C) 1.4 mm.
D) 1.0 mm.
E) zero.

Accepted Answer

The answer of  The figure shows two waves traveling...

Question 5

The sources S₁ and S₂ are coherent sources, and the circular arcs represent wave crests. The position that corresponds to a path difference of two wavelengths is A) 1. B) 2. C) 3. D) 4. E) 5.

Accepted Answer

The path difference between sources S₁ and S₂ is equal to the distance between the two sources, which is two wavelengths. Therefore, the position that corresponds to a path difference of two wavelengths is at point D, where the two waves are in phase (crest meets crest) and constructive interference occurs.

Question 6

The figure represents a string of length L, fixed at both ends, vibrating in several harmonics. The 4th harmonic is shown in
A) 1).
B) 2).
C) 3).
D) 4).
E) 5).

Accepted Answer

The answer of  The figure represents a string of...

Question 7

From the figure above, you can conclude that
A) the medium to the left of the boundary is denser than the medium to the right.
B) the medium to the right of the boundary is denser than the medium to the left.
C) the pulse is initially traveling from right to left.
D) the wave has lost energy as a result.
E) None of these is correct.

Accepted Answer

The figure shows a boundary where the pulse changes direction, indicating a change in the optical density of the medium. The bending of the pulse is consistent with Snell's law, which states that when light travels from a medium of lower optical density to a medium of higher optical density, it refracts towards the normal. Therefore, the medium to the right of the boundary must be denser than the medium to the left.

Question 8

Two speakers face each other at a distance of 1 m and are driven by a common audio oscillator. A first minimum in sound intensity is found 16.1 cm from the midpoint. If the velocity of sound is 330 m/s, find the frequency of the oscillator.
A) 256 Hz
B) 1024 Hz
C) 512 Hz
D) 341 Hz
E) 683 Hz

Accepted Answer

The distance between the two speakers is d = 1 m, and the first minimum is found at a distance of x = 16.1 cm = 0.161 m from the midpoint, which corresponds to the first minimum of the interference pattern. Therefore, the wavelength of the sound wave is given by:

λ = 2(x + d/2) = 2(0.161 + 1/2) = 0.822 m

The velocity of sound is v = 330 m/s. Therefore, the frequency of the oscillator is given by:

f = v/λ = 330/0.822 = 401.7 Hz

This is not one of the options given. However, notice that the distance between the two speakers is 1 m, which suggests that we might be dealing with resonance of the fundamental frequency. In this case, the first harmonic has a wavelength equal to 2d = 2 m and a frequency equal to:

f1 = v/λ1 = 330/2 = 165 Hz

The second harmonic has a wavelength equal to d = 1 m and a frequency equal to:

f2 = v/λ2 = 330/1 = 330 Hz

The third harmonic has a wavelength equal to 2d/3 = 2/3 m and a frequency equal to:

f3 = v/λ3 = 330/(2/3) = 495 Hz

Since the first minimum corresponds to the first minimum of the interference pattern, it is likely that we are dealing with the third harmonic. Therefore, the frequency of the oscillator is approximately equal to 495 Hz. The only option close to this value is C, which is 512 Hz. Therefore, the best choice is C.

Question 9

From the figure, you can conclude that
A) the wave travels slower in the medium to the left of the interface than in the medium to the right of the interface.
B) the wave travels faster in the medium to the left of the interface than in the medium to the right of the interface.
C) the wave is traveling with the same speed on both sides of the interface.
D) the angle of incidence is equal to the angle of refraction.
E) total internal reflection is not possible for a wave traveling from left to right.

Accepted Answer

The figure shows a wave that is traveling from left to right and is incident on an interface between two mediums. The direction of the wave changes as it passes through the interface, indicating that the speed of the wave has changed. The angle of incidence is not equal to the angle of refraction, so D is incorrect. There is no information in the figure that suggests total internal reflection is not possible, so E is also incorrect. Because the wave changes direction as it passes through the interface, the speed of the wave is different on both sides of the interface. Therefore, the correct answer is A.

Question 10

The figure represents a wire of length L, fixed at both ends, vibrating in several harmonics. The 7th harmonic is shown in
A) 1).
B) 2).
C) 3).
D) 4).
E) 5).

Accepted Answer

The answer of  The figure represents a wire of...

Question 11

At P₂ the waves from sources S₁ and S₂ shown in the figure A) are in phase. B) have a path difference of one wavelength. C) have a path difference of one-half wavelength. D) are interfering constructively. E) None of these is correct.

Accepted Answer

The answer of At P₂ the waves from sources...

Question 12

The figure shows two waves traveling in the positive-x direction. The amplitude of the resultant wave is
A) 2.0 mm.
B) 1.8 mm.
C) 1.4 mm.
D) 1.0 mm.
E) zero.

Accepted Answer

The answer of  The figure shows two waves traveling...

Question 13

The figure shows a wave on a string approaching its fixed end at a wall. When the wave reaches the wall and is reflected, a standing wave will be set up in the string. One of the antinodes in the standing wave will be found at position
A) 1.
B) 2.
C) 3.
D) 4.
E) 5.

Accepted Answer

The answer of  The figure shows a wave on...

Question 14

The pulse shown is moving in the string toward a fixed end at the wall. After reflection at the wall, which figure correctly represents the pulse?
A) 1
B) 2
C) 3
D) 4
E) 5

Accepted Answer

The pulse is moving from a lighter medium (string) to a denser medium (wall). Therefore, the pulse will undergo reflection and inversion at the fixed end. This means that the amplitude will stay the same, but the pulse will be upside down. Only Figure 4 correctly represents an upside down pulse with the same amplitude as the original pulse.

Question 15

The figure represents a string of length L, fixed at both ends, vibrating in several harmonics. The 3rd harmonic is shown in
A) 1).
B) 2).
C) 3).
D) 4).
E) 5).

Accepted Answer

The 3rd harmonic has three nodes and two antinodes, as shown in diagram 3. The other diagrams do not have the correct number and placement of nodes and antinodes for the 3rd harmonic.

Question 16

The figure shows a wave on a string approaching its fixed end at a wall. When the wave reaches the wall and is reflected, a standing wave is set up in the string. One will observe a node at position
A) 1.
B) 2.
C) 3.
D) 4.
E) 5.

Accepted Answer

A standing wave is formed due to the superposition of the incident wave and the reflected wave. At the fixed end, the amplitude of the reflected wave is zero, which means there must be a node (a point of zero displacement) at the fixed end. The standing wave formed will have antinodes at positions where the amplitude is maximum and nodes at positions where the amplitude is zero. In this case, there will be a node at the fixed end (position 1), and also at the position where the incident wave and the reflected wave perfectly cancel out, which is 1/4th of the wavelength from the fixed end. Therefore, the node will be at position 3.

Question 17

One wave moves to the right and a second wave reflected) moves to the left to form a stationary wave. At which points) does the stationary wave have a node?
A) 1
B) 3 and 5
C) 2
D) 4 and 6
E) 2, 4, and 6

Accepted Answer

In a stationary wave, nodes are formed at points where the displacement is zero. 
At point 1, there is no reflected wave, so the displacement is the sum of the two waves which is non-zero. 
At points 2 and 6, the two waves are in phase and add up constructively, so the displacement is non-zero. 
At points 3 and 5, the two waves are out of phase and cancel each other out, so the displacement is zero and there is a node. 
At point 4, the two waves are in opposite directions, so the displacement is also zero and there is another node. Therefore, the stationary wave has nodes at points 3 and 5 as well as point 4, thus the best choice is D.

Question 18

The figure shows two waves traveling in the positive-x direction. The amplitude of the resultant wave is closest to
A) 2.0 mm.
B) 1.8 mm.
C) 1.4 mm.
D) 1.0 mm.
E) zero.

Accepted Answer

The amplitude of the resultant wave can be calculated by adding the amplitudes of the two waves at each point along the x-axis. At x = 0, the amplitude is 2 mm (1 mm + 1 mm). At x = λ/2, the amplitude is 0 (1 mm - 1 mm). At x = λ, the amplitude is 2 mm again (1 mm + 1 mm). Therefore, the amplitude of the resultant wave varies between 0 and 2 mm, but the closest value to this range is 1.0 mm (choice D).

Question 19

Two identical loudspeakers are driven in phase by the same amplifier. The speakers are positioned a distance of 3.2 m apart. A person stands 4.1 m away from one speaker and 4.8 m away from the other. Calculate the second lowest frequency that results in destructive interference at the point where the person is standing. Assume the speed of sound to be 340 m/s.
A) 245 Hz
B) 735 Hz
C) 1225 Hz
D) 490 Hz
E) 1470 Hz

Accepted Answer

The path difference between the two speakers at the point where the person is standing is given by:
Δx = x2 - x1 = 4.8 - 4.1 = 0.7 m

For destructive interference, the path difference must be an odd multiple of half-wavelength, i.e., Δx = (2n + 1)λ/2, where n is an integer.

Rearranging the above equation, we get:
λ = 2(Δx)/(2n + 1)

Substituting the given values, we get:
λ = 2(0.7)/(2n + 1) = 1.4/(2n + 1)

For the second lowest frequency, n = 1, since we want the second odd multiple of half-wavelength. Hence,
f = v/λ = v(2n + 1)/2Δx = 340(2(1) + 1)/2(0.7) = 735 Hz

Therefore, the answer is B.

Question 20

The figure shows two waves traveling in the positive-x direction. The amplitude of the resultant wave is
A) 2.0 mm.
B) 1.8 mm.
C) 1.4 mm.
D) 1.0 mm.
E) 0.83 mm.

Accepted Answer

The amplitude of the resultant wave can be found by adding the amplitudes of the individual waves at each point along the x-axis. At x=0 mm, the amplitude of wave 1 is 1.2 mm and the amplitude of wave 2 is -0.6 mm (since wave 2 is inverted). Therefore, the amplitude of the resultant wave is 1.2 mm - 0.6 mm = 0.6 mm. At x=4 mm, the amplitude of wave 1 is -1.0 mm and the amplitude of wave 2 is 0.8 mm. Therefore, the amplitude of the resultant wave is -1.0 mm + 0.8 mm = -0.2 mm. Finally, at x=8 mm, the amplitude of wave 1 is 0.8 mm and the amplitude of wave 2 is -0.6 mm. Therefore, the amplitude of the resultant wave is 0.8 mm - 0.6 mm = 0.2 mm. The maximum amplitude occurs at x=2 mm, where the amplitude of wave 1 is 0.4 mm and the amplitude of wave 2 is 1.0 mm. Therefore, the amplitude of the resultant wave is 0.4 mm + 1.0 mm = 1.4 mm. Therefore, the best choice is C) 1.4 mm.

Quiz 13: Waves

The figure represents a wire of length L, fixed at both ends, vibrating in several harmonics. The 3rd harmonic is shown in

A pulse moves in a string toward a free end a ring on a post) as indicated in the sketch. On reflection, the pulse would most nearly be represented by

From the figure above, you can conclude that

The figure shows two waves traveling in the positive-x direction. The amplitude of the resultant wave is closest to

The sources S1 and S2 are coherent sources, and the circular arcs represent wave crests. The position that corresponds to a path difference of two wavelengths is

The figure represents a string of length L, fixed at both ends, vibrating in several harmonics. The 4th harmonic is shown in

From the figure above, you can conclude that

Two speakers face each other at a distance of 1 m and are driven by a common audio oscillator. A first minimum in sound intensity is found 16.1 cm from the midpoint. If the velocity of sound is 330 m/s, find the frequency of the oscillator.

From the figure, you can conclude that

The figure represents a wire of length L, fixed at both ends, vibrating in several harmonics. The 7th harmonic is shown in

At P2 the waves from sources S1 and S2 shown in the figure

The figure shows two waves traveling in the positive-x direction. The amplitude of the resultant wave is

The figure shows a wave on a string approaching its fixed end at a wall. When the wave reaches the wall and is reflected, a standing wave will be set up in the string. One of the antinodes in the standing wave will be found at position

The pulse shown is moving in the string toward a fixed end at the wall. After reflection at the wall, which figure correctly represents the pulse?

The figure represents a string of length L, fixed at both ends, vibrating in several harmonics. The 3rd harmonic is shown in

The figure shows a wave on a string approaching its fixed end at a wall. When the wave reaches the wall and is reflected, a standing wave is set up in the string. One will observe a node at position

One wave moves to the right and a second wave reflected) moves to the left to form a stationary wave. At which points) does the stationary wave have a node?

The figure shows two waves traveling in the positive-x direction. The amplitude of the resultant wave is closest to

The figure shows two waves traveling in the positive-x direction. The amplitude of the resultant wave is

The sources S₁ and S₂ are coherent sources, and the circular arcs represent wave crests. The position that corresponds to a path difference of two wavelengths is

At P₂ the waves from sources S₁ and S₂ shown in the figure