Question 1

Two canoes are 10 m apart on a lake. Each bobs up and down with a period of 8.0 seconds. When one canoe is at its highest point, the other canoe is at its lowest point. Both canoes are always within a single cycle of the waves. Determine the speed of the waves.
A)2.5 m/s
B)1.3 m/s
C)5.0 m/s
D)0.65 m/s
E)0.75 m/s

Accepted Answer

The canoes are half a wavelength apart because one is at the highest point and the other at the lowest. Therefore, the full wavelength is 20 m. With a period of 8.0 seconds, the wave speed is wavelength/period = 20 m / 8 s = 2.5 m/s.

Question 2

Which one of the following statements concerning waves is false?
A)A wave can have both transverse and longitudinal components.
B)A wave carries energy from one place to another.
C)A wave does not result in the bulk flow of the material of its medium.
D)A wave is a traveling disturbance.
E)A transverse wave is one in which the disturbance is parallel to the direction of travel.

Accepted Answer

A transverse wave is one in which the disturbance is perpendicular to the direction of travel, not parallel.

Question 3

Which one of the following waves is purely longitudinal?
A)sound waves in air
B)microwaves traveling through air
C)radio waves traveling through vacuum
D)waves on a plucked violin string
E)surface waves in a shallow pan of water

Accepted Answer

Sound waves in air are purely longitudinal waves as they propagate by compressing and rarefying the medium in the same direction as the wave travels. The other options listed are not purely longitudinal waves.

Question 4

A periodic wave travels along a stretched string in the direction shown by the arrow. The sketch shows a "snapshot" of the pulse at a certain instant. Points A, B, and C are on the string. Which entry in the table below correctly describes how particles of string between A and B and between B and C are moving?  between A and B between B and C
A)down down
B)up down
C)left right
D)up up
E)down up

Accepted Answer

Since the wave is a pulse traveling in the direction shown by the arrow, particles in the region between A and B would be moving upwards (as evidenced by the upward displacement of the string) while particles between B and C would be moving downwards (as evidenced by the downward displacement of the string). Therefore, the correct choice is B - up down.

Question 5

A wave moves at a constant speed along a string. Which one of the following statements is false concerning the motion of particles in the string?
A)The particle speed is constant.
B)The particle speed is not the same as the wave speed.
C)The particle speed depends on the amplitude of the periodic motion of the source.
D)The particle speed depends on the frequency of the periodic motion of the source.
E)The particle speed is independent of the tension and linear density of the string.

Accepted Answer

The answer of A wave moves at a constant speed...

Question 6

What is the wavelength of a wave with a speed of 9.0 m/s and a period of 0.33 s?
A)0.33 m
B)1.5 m
C)3.0 m
D)13 m
E)27 m

Accepted Answer

The wavelength can be calculated using the formula: Wavelength = Speed × Period. Substituting the given values: Wavelength = 9.0 m/s × 0.33 s = 2.97 m, which rounds to 3.0 m.

Question 7

The speed of sound in a certain metal block is 2.00 × 10³ m/s. The graph shows the amplitude (in meters) of a wave traveling through the block versus time (in milliseconds). What is the wavelength of this wave? A)0.5 m B)1.5 m C)3.0 m D)4.0 m E)6.0 m

Accepted Answer

The answer of The speed of sound in a certain...

Question 8

The tension in a taut rope is increased by a factor of 9. How does the speed of wave pulses on the rope change, if at all?
A)The speed remains the same.
B)The speed is reduced by a factor of 3.
C)The speed is reduced by a factor of 9.
D)The speed is increased by a factor of 3.
E)The speed is increased by a factor of 9.

Accepted Answer

The speed of wave pulses on a rope is proportional to the square root of the tension. If the tension is increased by a factor of 9, the speed increases by the square root of 9, which is 3.

Question 9

A wave has a frequency of 58 Hz and a speed of 31 m/s. What is the wavelength of this wave?
A)1.9 m
B)3.5 m
C)0.29 m
D)0.53 m
E)31 m

Accepted Answer

The wavelength of a wave can be found using the formula: 
wavelength = speed/frequency

Substituting the given values: 
wavelength = 31/58 
wavelength = 0.53 m

Therefore, the correct answer is D) 0.53 m.

Question 10

A periodic wave is produced on a stretched string. Which one of the following properties is not related to the speed of the wave?
A)frequency
B)amplitude
C)period
D)wavelength
E)tension in the string

Accepted Answer

The speed of a wave is determined by the properties of the medium, such as tension and density, and not by its amplitude. The frequency, period, wavelength, and tension all play a role in determining the speed of a wave on a stretched string.

Question 11

The displacement of a vibrating string versus position along the string is shown in the figure. The periodic waves have a speed of 10.0 cm/s. A and B are two points on the string. 
-What is the frequency of the wave?
A)0.60 Hz
B)0.90 Hz
C)1.1 Hz
D)1.3 Hz
E)1.7 Hz

Accepted Answer

The answer of The displacement of a vibrating string versus...

Question 12

A certain string on a piano is tuned to produce middle C (f = 261.63 Hz) by carefully adjusting the tension in the string. For a fixed wavelength, what is the frequency when this tension is tripled?
A)87.21 Hz
B)151.05 Hz
C)370.00 Hz
D)453.16 Hz
E)784.89 Hz

Accepted Answer

The frequency of a string is proportional to the square root of the tension. Tripling the tension increases the frequency by a factor of √3. Thus, the new frequency is 261.63 Hz * √3 ≈ 453.16 Hz.

Question 13

A transverse periodic wave described by the expression  (where y and x are in meters and t is in seconds) is established on a string. Which one of the following statements concerning this wave is false?
A)The wave is traveling in the negative x direction.
B)The amplitude is 1.0 m.
C)The frequency of the wave is 0.10 Hz.
D)The wavelength of this wave is 2.0 m.
E)The wave travels with speed 5.0 m/s.

Accepted Answer

The answer of A transverse periodic wave described by the...

Question 14

The displacement of a vibrating string versus position along the string is shown in the figure. The periodic waves have a speed of 10.0 cm/s. A and B are two points on the string. 
-What is the difference in phase between the points A and B?
A)($\pi$/4)radians
B)($\pi$/2)radians
C)$\pi$radians
D)(3$\pi$/4)radians
E)2$\pi$ radians

Accepted Answer

The answer of The displacement of a vibrating string versus...

Question 15

The displacement of a vibrating string versus position along the string is shown in the figure. The periodic waves have a speed of 10.0 cm/s. A and B are two points on the string. 
-What is the amplitude of the wave?
A)2 mm
B)4 mm
C)8 mm
D)12 mm
E)16 mm

Accepted Answer

The answer of The displacement of a vibrating string versus...

Question 16

A steel wire of mass 0.400 kg and length 0.640 m supports a 102-kg block. The wire is struck exactly at its midpoint causing a small displacement. How long does it take the peak of this displacement to reach the top of the wire? A)2.00 × 10^-³ s B)4.00 × 10^-³ s C)6.00 × 10^-³ s D)8.00 × 10^-³ s E)1.60 × 10^-² s

Accepted Answer

The answer of A steel wire of mass 0.400 kg...

Question 17

The displacement of a vibrating string versus position along the string is shown in the figure. The periodic waves have a speed of 10.0 cm/s. A and B are two points on the string. 
-What is the wavelength of the wave?
A)3.0 cm
B)6.0 cm
C)9.0 cm
D)12 cm
E)15 cm

Accepted Answer

The wavelength is the distance between two consecutive peaks (or troughs) of the wave. From the graph, we can see that the distance between point A and point B is one wavelength. Thus, the wavelength is the distance between A and B, which is approximately 6.0 cm.

Question 18

A wave has an amplitude of 0.35 m, a frequency of 1.05 × 10⁶ Hz, and travels in the positive x direction at the speed of light, 3.00 × 10⁸ m/s. Which one of the following equations correctly represents this wave? A)y = 0.35 sin (6.60 × 10⁶t - 0.022x) B)y = 0.35 sin (6.60 × 10⁶t + 0.022x) C)y = 0.35 sin (286t - 1.05 × 10⁶x) D)y = 0.35 sin (286t + 1.05 × 10⁶x) E)y = 0.35 sin (1.05 × 10⁶t + 3.00 × 10⁸x)

Accepted Answer

The correct equation for a wave traveling in the positive x direction is:y = A sin (2πft - 2πx/λ)where:A is the amplitude of the wavef is the frequency of the wavet is the timex is the positionλ is the wavelength of the waveIn this case, the amplitude is 0.35 m, the frequency is 1.05 × 10^6 Hz, and the speed of the wave is 3.00 × 10^8 m/s. The wavelength can be calculated using the formula:λ = v/fwhere v is the speed of the wave and f is the frequency.Substituting the given values into the formula, we get:λ = 3.00 × 10^8 m/s / 1.05 × 10^6 Hz = 285.71 mNow we can substitute all of the values into the equation for the wave:y = 0.35 sin (2π(1.05 × 10^6 Hz)t - 2πx/285.71 m)Simplifying, we get:y = 0.35 sin (6.60 × 10^6t - 0.022x)Therefore, the correct answer is A.

Question 19

A wave is traveling at 35 m/s on a string with a linear density of 0.082 kg/m. What is the tension in the string?
A)0.28 N
B)0.56 N
C)2.5 N
D)5.0 N
E)10 N

Accepted Answer

The wave speed v on a string is given by the formula v = sqrt(T/μ), where T is the tension and μ is the linear density. Rearranging for T gives T = v^2 * μ. Substituting the given values, T = (35 m/s)^2 * 0.082 kg/m = 100.45 N, which rounds to 10 N.

Question 20

Of the three traveling waves listed below, which one(s) is(are) traveling in the +x direction? 
A)1 only
B)2 only
C)3 only
D)1, 2, and 3
E)2 and 3 only

Accepted Answer

In a transverse wave, the displacement of the medium is perpendicular to the direction of the wave. In a longitudinal wave, the displacement of the medium is parallel to the direction of the wave. 
Wave 2 is a transverse wave with oscillations perpendicular to the x-axis, meaning that it is traveling in the +x direction. 
Wave 1 and Wave 3 are longitudinal waves, with compressions and rarefactions along the direction of the wave. Wave 1 is traveling in the -x direction and Wave 3 is traveling in the -y direction.

Quiz 16: Waves and Sound

Two canoes are 10 m apart on a lake. Each bobs up and down with a period of 8.0 seconds. When one canoe is at its highest point, the other canoe is at its lowest point. Both canoes are always within a single cycle of the waves. Determine the speed of the waves.

Which one of the following statements concerning waves is false?

Which one of the following waves is purely longitudinal?

A wave moves at a constant speed along a string. Which one of the following statements is false concerning the motion of particles in the string?

What is the wavelength of a wave with a speed of 9.0 m/s and a period of 0.33 s?

The speed of sound in a certain metal block is 2.00 × 10³ m/s. The graph shows the amplitude (in meters) of a wave traveling through the block versus time (in milliseconds) . What is the wavelength of this wave?

The tension in a taut rope is increased by a factor of 9. How does the speed of wave pulses on the rope change, if at all?

A wave has a frequency of 58 Hz and a speed of 31 m/s. What is the wavelength of this wave?

A periodic wave is produced on a stretched string. Which one of the following properties is not related to the speed of the wave?

The displacement of a vibrating string versus position along the string is shown in the figure. The periodic waves have a speed of 10.0 cm/s. A and B are two points on the string. -What is the frequency of the wave?

A certain string on a piano is tuned to produce middle C (f = 261.63 Hz) by carefully adjusting the tension in the string. For a fixed wavelength, what is the frequency when this tension is tripled?

A transverse periodic wave described by the expression (where y and x are in meters and t is in seconds) is established on a string. Which one of the following statements concerning this wave is false?

The displacement of a vibrating string versus position along the string is shown in the figure. The periodic waves have a speed of 10.0 cm/s. A and B are two points on the string. -What is the amplitude of the wave?

A steel wire of mass 0.400 kg and length 0.640 m supports a 102-kg block. The wire is struck exactly at its midpoint causing a small displacement. How long does it take the peak of this displacement to reach the top of the wire?

The displacement of a vibrating string versus position along the string is shown in the figure. The periodic waves have a speed of 10.0 cm/s. A and B are two points on the string. -What is the wavelength of the wave?

A wave has an amplitude of 0.35 m, a frequency of 1.05 × 10⁶ Hz, and travels in the positive x direction at the speed of light, 3.00 × 10⁸ m/s. Which one of the following equations correctly represents this wave?

A wave is traveling at 35 m/s on a string with a linear density of 0.082 kg/m. What is the tension in the string?

Of the three traveling waves listed below, which one(s) is(are) traveling in the +x direction?

Quiz 16: Waves and Sound

Two canoes are 10 m apart on a lake. Each bobs up and down with a period of 8.0 seconds. When one canoe is at its highest point, the other canoe is at its lowest point. Both canoes are always within a single cycle of the waves. Determine the speed of the waves.

Which one of the following statements concerning waves is false?

Which one of the following waves is purely longitudinal?

A wave moves at a constant speed along a string. Which one of the following statements is false concerning the motion of particles in the string?

What is the wavelength of a wave with a speed of 9.0 m/s and a period of 0.33 s?

The speed of sound in a certain metal block is 2.00 × 103 m/s. The graph shows the amplitude (in meters) of a wave traveling through the block versus time (in milliseconds) . What is the wavelength of this wave?

The tension in a taut rope is increased by a factor of 9. How does the speed of wave pulses on the rope change, if at all?

A wave has a frequency of 58 Hz and a speed of 31 m/s. What is the wavelength of this wave?

A periodic wave is produced on a stretched string. Which one of the following properties is not related to the speed of the wave?

The displacement of a vibrating string versus position along the string is shown in the figure. The periodic waves have a speed of 10.0 cm/s. A and B are two points on the string. -What is the frequency of the wave?

A certain string on a piano is tuned to produce middle C (f = 261.63 Hz) by carefully adjusting the tension in the string. For a fixed wavelength, what is the frequency when this tension is tripled?

A transverse periodic wave described by the expression (where y and x are in meters and t is in seconds) is established on a string. Which one of the following statements concerning this wave is false?

The displacement of a vibrating string versus position along the string is shown in the figure. The periodic waves have a speed of 10.0 cm/s. A and B are two points on the string. -What is the difference in phase between the points A and B?

The displacement of a vibrating string versus position along the string is shown in the figure. The periodic waves have a speed of 10.0 cm/s. A and B are two points on the string. -What is the amplitude of the wave?

A steel wire of mass 0.400 kg and length 0.640 m supports a 102-kg block. The wire is struck exactly at its midpoint causing a small displacement. How long does it take the peak of this displacement to reach the top of the wire?

The displacement of a vibrating string versus position along the string is shown in the figure. The periodic waves have a speed of 10.0 cm/s. A and B are two points on the string. -What is the wavelength of the wave?

A wave has an amplitude of 0.35 m, a frequency of 1.05 × 106 Hz, and travels in the positive x direction at the speed of light, 3.00 × 108 m/s. Which one of the following equations correctly represents this wave?

A wave is traveling at 35 m/s on a string with a linear density of 0.082 kg/m. What is the tension in the string?

Of the three traveling waves listed below, which one(s) is(are) traveling in the +x direction?

The speed of sound in a certain metal block is 2.00 × 10³ m/s. The graph shows the amplitude (in meters) of a wave traveling through the block versus time (in milliseconds) . What is the wavelength of this wave?

A wave has an amplitude of 0.35 m, a frequency of 1.05 × 10⁶ Hz, and travels in the positive x direction at the speed of light, 3.00 × 10⁸ m/s. Which one of the following equations correctly represents this wave?