Question 1

The transverse wave shown is traveling from left to right in a medium. The direction of the instantaneous velocity of the medium at point P is:

Accepted Answer

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Question 2

Two identical but separate strings, with the same tension, carry sinusoidal waves with the same frequency. Wave A has an amplitude that is twice that of wave B and transmits energy at a rate that is __________ that of wave B.

Accepted Answer

The energy transmitted by a wave is proportional to the square of its amplitude. Since wave A has twice the amplitude of wave B, its energy is (2^2) = 4 times that of wave B. Therefore, the correct answer is D: four times.

Question 3

Any point on a string carrying a sinusoidal wave is moving with its maximum speed when:

Accepted Answer

The maximum speed of a point on a string carrying a sinusoidal wave occurs when the magnitude of its displacement is at a minimum. This is because the velocity of the point is proportional to the derivative of the displacement, which is itself a sinusoidal wave. The velocity is zero at the maximum and minimum points of the displacement, and is maximum at the zero points of the displacement. Therefore, the point on the string is moving with its maximum speed when the magnitude of its displacement is at a minimum.

Question 4

A wave traveling to the right on a stretched string is shown below. The direction of the instantaneous velocity of the point P on the string is:

Accepted Answer

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Question 5

The tension in a string with a linear density of 0.0010 kg/m is 0.40 N. A 100 Hz sinusoidal wave on this string has a wavelength of:

Accepted Answer

The speed of a wave on a string is given by v = sqrt(T/u), where T is the tension and u is the linear density. 
v = sqrt(0.40 N / 0.0010 kg/m) = 20 m/s

The wavelength is given by lambda = v/f, where f is the frequency.
lambda = 20 m/s / 100 Hz = 0.20 m = 20 cm.

Therefore, the wavelength of the wave on this string is 20 cm, which corresponds to choice D.

Question 6

The diagram shows three identical strings that have been put under tension by suspending masses of 5 kg each. For which is the wave speed the greatest?

Accepted Answer

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Question 7

A long string is constructed by joining the ends of 2 shorter strings. The tension in the strings is the same but string I has 4 times the linear mass density of string II. When a sinusoidal wave passes from string I to string II:

Accepted Answer

The wave speed in a string is given by $ v = \sqrt{\frac{T}{\mu}} $, where $ T $ is the tension and $ \mu $ is the linear mass density. Since the tension is the same and string I has 4 times the linear mass density of string II, the wave speed in string II will be twice that in string I.

Question 8

A source of frequency f sends waves of wavelength $\lambda$ traveling with speed v in some medium. If the frequency is changed from f to 2f, then the new wavelength and new speed are (respectively):

Accepted Answer

The speed of wave propagation in a medium is constant for a given frequency and does not depend on the frequency. Therefore, if the frequency is doubled, the wavelength is halved to maintain the same wave speed.

Question 9

A long string is constructed by joining the ends of two shorter strings. The tension in the strings is the same but string I has 4 times the linear mass density of string II. When a sinusoidal wave passes from string I to string II:

Accepted Answer

When a wave passes from one medium to another, the frequency remains the same but the wavelength changes based on the ratio of the speeds of the waves in each medium. The speed of a wave is proportional to the square root of the tension divided by the linear mass density. Since the tension is the same and string I has 4 times the linear mass density of string II, the speed of a wave in string II is 2 times that in string I. Therefore, the wavelength in string II is half that in string I, so the wavelength decreases by a factor of 2.

Question 10

The time required for a small pulse to travel from A to B on a stretched cord shown is NOT altered by changing:

Accepted Answer

The speed of a pulse traveling along a stretched cord depends on the tension in the cord and the linear mass density of the cord, not on the shape of the pulse.

Question 11

The mathematical forms for the three sinusoidal traveling waves are gives by  where x is in meters and t is in seconds. Of these waves:

Accepted Answer

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Question 12

Here are the equations for the three waves traveling on separate strings. Rank them according to the maxium transverse speed, least to greatest.

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Question 13

Suppose the maximum speed of a string carrying a sinusoidal wave is v_s. When the displacement of a point on the string is half its maximum, the speed of the point is:

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Question 14

When a 100-Hz oscillator is used to generate a sinusoidal wave on a certain string the wavelength is 10 cm. When the tension in the string is doubled the generator produces a wave with a frequency and wavelength of:

Accepted Answer

The speed of the wave on the string is given by the equation v = fλ, where v is the speed, f is the frequency, and λ is the wavelength. Since the frequency is constant at 100 Hz, and the wavelength is initially 10 cm, we can solve for the speed: 
v = fλ = (100 Hz)(10 cm) = 1000 cm/s

When the tension in the string is doubled, the speed of the wave will also double (assuming the mass per unit length remains the same). So the speed of the wave is now: 
v' = 2v = 2000 cm/s

To find the new wavelength, we can use the equation v' = f'λ', where f' is the new frequency: 
2000 cm/s = f'(λ')

We know that the new frequency f' is greater than 100 Hz, since the speed has increased. We can try the answer choices:

A) 200 Hz and 20 cm 
Using f' = 200 Hz, we get λ' = v'/f' = 2000/200 = 10 cm 
This matches the initial wavelength, so this is not the correct answer.

B) 141 Hz and 10 cm 
Using f' = 141 Hz, we get λ' = v'/f' = 2000/141 = 14.2 cm 
This is close to the initial wavelength, but not quite there.

C) 100 Hz and 20 cm 
Using f' = 100 Hz, we get λ' = v'/f' = 2000/100 = 20 cm 
This does not match the initial wavelength, so this is not the correct answer.

D) 100 Hz and 14 cm 
Using f' = 100 Hz, we get λ' = v'/f' = 2000/100 = 20 cm 
This is the same as the initial wavelength, which means it must be the answer.

E) 50 Hz and 14 cm 
Using f' = 50 Hz, we get λ' = v'/f' = 2000/50 = 40 cm 
This does not match the initial wavelength, so this is not the correct answer.

Therefore, the answer is D: 100 Hz and 14 cm.

Question 15

A sinusoidal wave is generated by moving the end of a string up and down periodically. The generator must supply the greatest power when the end of the string:

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Question 16

A sinusoidal wave is generated by moving the end of a string up and down periodically. The generator does not supply any power when the end of the string

Accepted Answer

The generator does not supply any power when the end of the string has its greatest displacement because at this point, the velocity of the string is zero (it momentarily stops before changing direction), and power is related to the rate of doing work or energy transfer, which involves both force and velocity.

Question 17

Two identical but separate strings, with the same tension, carry sinusoidal waves with the same amplitude. Wave A has a frequency that is twice that of wave B and transmits energy at a rate that is __________ that of wave B.

Accepted Answer

The rate at which energy is transmitted by a wave (the power) is proportional to the square of both the amplitude and the frequency. Since the amplitude is the same for both waves but the frequency of wave A is twice that of wave B, the energy transmitted by wave A is $2^2 = 4$ times that of wave B.

Question 18

The speed of a sinusoidal wave on a string depends on:

Accepted Answer

The speed of a sinusoidal wave on a string is directly proportional to the tension in the string. This means that if the tension in the string is increased, the wave speed will also increase. Alternatively, if the tension in the string is decreased, the wave speed will also decrease. The frequency, wavelength, length, and amplitude of the wave do not affect the wave speed on a string, only the shape and characteristics of the wave itself.

Question 19

A string carries a sinusoidal wave with an amplitude of 2.0 cm and a frequency of 100 Hz. The maximum speed of any point on the string is:

Accepted Answer

The answer of A string carries a sinusoidal wave with...

Question 20

Three separate strings are made of the same material. String 1 has length L and tension  $ \tau $, string 2 has length 2L and tension 2 $ \tau $ and string 3 has length 3L and tension 3 $ \tau $. A pulse is started at one end of each string. If the pulses start at the same time, the order in which they reach the other end is:

Accepted Answer

The speed of a wave on a string is given by v = sqrt(T/μ), where T is the tension and μ is the linear density. Since all three strings are made of the same material, they have the same linear density. Therefore, the speed of the wave on each string is proportional to the square root of the tension. Since string 1 has the lowest tension, it will have the lowest wave speed. String 2 has twice the tension of string 1, so it will have a wave speed that is sqrt(2) times faster than string 1. String 3 has three times the tension of string 1, so it will have a wave speed that is sqrt(3) times faster than string 1. Therefore, the order in which the pulses reach the other end is 1, 2, 3.

Quiz 16: Waves I

Two identical but separate strings, with the same tension, carry sinusoidal waves with the same frequency. Wave A has an amplitude that is twice that of wave B and transmits energy at a rate that is __________ that of wave B.

Any point on a string carrying a sinusoidal wave is moving with its maximum speed when:

The tension in a string with a linear density of 0.0010 kg/m is 0.40 N. A 100 Hz sinusoidal wave on this string has a wavelength of:

The diagram shows three identical strings that have been put under tension by suspending masses of 5 kg each. For which is the wave speed the greatest?

A long string is constructed by joining the ends of 2 shorter strings. The tension in the strings is the same but string I has 4 times the linear mass density of string II. When a sinusoidal wave passes from string I to string II:

A source of frequency f sends waves of wavelength $\lambda$ traveling with speed v in some medium. If the frequency is changed from f to 2f, then the new wavelength and new speed are (respectively) :

A long string is constructed by joining the ends of two shorter strings. The tension in the strings is the same but string I has 4 times the linear mass density of string II. When a sinusoidal wave passes from string I to string II:

The time required for a small pulse to travel from A to B on a stretched cord shown is NOT altered by changing:

The mathematical forms for the three sinusoidal traveling waves are gives by where x is in meters and t is in seconds. Of these waves:

Here are the equations for the three waves traveling on separate strings. Rank them according to the maxium transverse speed, least to greatest.

Suppose the maximum speed of a string carrying a sinusoidal wave is v_s. When the displacement of a point on the string is half its maximum, the speed of the point is:

When a 100-Hz oscillator is used to generate a sinusoidal wave on a certain string the wavelength is 10 cm. When the tension in the string is doubled the generator produces a wave with a frequency and wavelength of:

A sinusoidal wave is generated by moving the end of a string up and down periodically. The generator must supply the greatest power when the end of the string:

A sinusoidal wave is generated by moving the end of a string up and down periodically. The generator does not supply any power when the end of the string

Two identical but separate strings, with the same tension, carry sinusoidal waves with the same amplitude. Wave A has a frequency that is twice that of wave B and transmits energy at a rate that is __________ that of wave B.

The speed of a sinusoidal wave on a string depends on:

A string carries a sinusoidal wave with an amplitude of 2.0 cm and a frequency of 100 Hz. The maximum speed of any point on the string is:

Quiz 16: Waves I

The transverse wave shown is traveling from left to right in a medium. The direction of the instantaneous velocity of the medium at point P is:

Two identical but separate strings, with the same tension, carry sinusoidal waves with the same frequency. Wave A has an amplitude that is twice that of wave B and transmits energy at a rate that is __________ that of wave B.

Any point on a string carrying a sinusoidal wave is moving with its maximum speed when:

A wave traveling to the right on a stretched string is shown below. The direction of the instantaneous velocity of the point P on the string is:

The tension in a string with a linear density of 0.0010 kg/m is 0.40 N. A 100 Hz sinusoidal wave on this string has a wavelength of:

The diagram shows three identical strings that have been put under tension by suspending masses of 5 kg each. For which is the wave speed the greatest?

A long string is constructed by joining the ends of 2 shorter strings. The tension in the strings is the same but string I has 4 times the linear mass density of string II. When a sinusoidal wave passes from string I to string II:

A source of frequency f sends waves of wavelength λ\lambdaλ traveling with speed v in some medium. If the frequency is changed from f to 2f, then the new wavelength and new speed are (respectively) :

A long string is constructed by joining the ends of two shorter strings. The tension in the strings is the same but string I has 4 times the linear mass density of string II. When a sinusoidal wave passes from string I to string II:

The time required for a small pulse to travel from A to B on a stretched cord shown is NOT altered by changing:

The mathematical forms for the three sinusoidal traveling waves are gives by where x is in meters and t is in seconds. Of these waves:

Here are the equations for the three waves traveling on separate strings. Rank them according to the maxium transverse speed, least to greatest.

Suppose the maximum speed of a string carrying a sinusoidal wave is vs. When the displacement of a point on the string is half its maximum, the speed of the point is:

When a 100-Hz oscillator is used to generate a sinusoidal wave on a certain string the wavelength is 10 cm. When the tension in the string is doubled the generator produces a wave with a frequency and wavelength of:

A sinusoidal wave is generated by moving the end of a string up and down periodically. The generator must supply the greatest power when the end of the string:

A sinusoidal wave is generated by moving the end of a string up and down periodically. The generator does not supply any power when the end of the string

Two identical but separate strings, with the same tension, carry sinusoidal waves with the same amplitude. Wave A has a frequency that is twice that of wave B and transmits energy at a rate that is __________ that of wave B.

The speed of a sinusoidal wave on a string depends on:

A string carries a sinusoidal wave with an amplitude of 2.0 cm and a frequency of 100 Hz. The maximum speed of any point on the string is:

A source of frequency f sends waves of wavelength $\lambda$ traveling with speed v in some medium. If the frequency is changed from f to 2f, then the new wavelength and new speed are (respectively) :

Suppose the maximum speed of a string carrying a sinusoidal wave is v_s. When the displacement of a point on the string is half its maximum, the speed of the point is: