Question 1

To transmit four times as much energy per unit time along a string, you can

Accepted Answer

The answer of To transmit four times as much energy...

Question 2

You are holding on to one end of a long string that is fastened to a rigid steel light pole. After producing a wave pulse that was 5 mm high and 4 cm wide, you want to produce a pulse that is 6 cm wide and 7 mm high. You must move your hand up and down once,

Accepted Answer

In order to produce a wave pulse that is higher and wider, you need to produce a larger disturbance on the string. Therefore, you need to move your hand a greater distance up than before. However, since the pulse is also wider, you will need to take a longer time to produce the pulse. Consequently, choice D is the correct answer.

Question 3

The figure below represents a string which has a heavy section and a light section. The mass per unit length of the heavy section is 16 times as large as the mass per unit length of the light section. When the string is under tension, the speed of a pulse traveling in the heavy section is ____ times the speed of that same pulse traveling in the light section.

Accepted Answer

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

Question 4

Exhibit 16-3
Four wave functions are given below.
I.y(x, t) = 5sin(4x - 20t + 4)
II.y(x, t) = 5sin(3x - 12t + 5)
III.y(x, t) = 5cos(4x + 24t + 6)
IV.y(x, t) = 14cos(2x - 8t + 3)
Use this exhibit to answer the following question(s).
-Refer to Exhibit 16-3. Rank the wave functions in order of the magnitude of the wave speeds, from least to greatest.

Accepted Answer

The answer of Exhibit 16-3
Four wave functions are given below.
I.y(x,...

Question 5

A student attaches a length of nylon fishing line to a fence post. She stretches it out and shakes the end of the rope in her hand back and forth to produce waves on the line. The most efficient way for her to increase the wavelength is to

Accepted Answer

Increasing the tension on the line increases the wave speed, and shaking the end fewer times per second (decreasing frequency) increases the wavelength, as wavelength is directly proportional to wave speed and inversely proportional to frequency.

Question 6

Exhibit 16-1
The figure below shows a sine wave at one point of a string as a function of time.  Use the exhibit to answer the following question(s).
-Refer to Exhibit 16-1. Which of the graphs below shows a wave where the amplitude and frequency are each reduced in half?

Accepted Answer

The answer of Exhibit 16-1
The figure below shows a sine...

Question 7

You are holding on to one end of a long string that is fastened to a rigid steel light pole. After producing a wave pulse that was 5 mm high and 4 cm wide, you want to produce a pulse that is 4 cm wide but 7 mm high. You must move your hand up and down once,

Accepted Answer

To produce a wave pulse that is higher (7 mm instead of 5 mm), you need to move your hand a greater distance up. The width of the pulse (4 cm) is determined by the time it takes for your hand to move up and then down. Since the width of the pulse remains the same, the time taken for the hand movement should also remain the same.

Question 8

Exhibit 16-3
Four wave functions are given below.
I.y(x, t) = 5sin(4x - 20t + 4)
II.y(x, t) = 5sin(3x - 12t + 5)
III.y(x, t) = 5cos(4x + 24t + 6)
IV.y(x, t) = 14cos(2x - 8t + 3)
Use this exhibit to answer the following question(s).
-Refer to Exhibit 16-3. Rank the wave functions in order of the magnitude of the wavelengths, from least to greatest.

Accepted Answer

The wavelength ($\lambda$) of a wave is inversely proportional to the coefficient of $x$ in the wave function, given by the general form $y(x, t) = A\sin(kx - \omega t + \phi)$ or $y(x, t) = A\cos(kx - \omega t + \phi)$, where $k = 2\pi/\lambda$. For the given wave functions, the coefficients of $x$ are 4 for I and III, 3 for II, and 2 for IV. Thus, the order from least to greatest wavelength is I = III (same $k$, so same $\lambda$), II, and IV.

Question 9

Suppose that you were selected for a "Survivor"-type TV show. To help keep your group connected, you suggest that long vines can be tied together and used to transmit signals in cases of emergency. To get the signals to travel faster, you should

Accepted Answer

Both A and B are valid options to increase the speed of signal transmission through the vines. Lighter vines will have less mass to move, and increasing tension will help the energy of the signal travel faster through the stretched vine. However, hanging weights from the vines (option C) would actually slow down the transmission speed by adding more mass to the system. Therefore, either A or B (or both) would be the best choices.

Question 10

The wave equation is written down in an exam as  From dimensional considerations we see that

Accepted Answer

The answer of The wave equation is written down in...

Question 11

Find the period of a wave of 100-m wavelength in deep water where  .

Accepted Answer

The answer of Find the period of a wave of...

Question 12

Ariel claims that a pulse is described by the equation  where x and y are measured in cm and t in s. Miranda says that it is not possible to represent a pulse with this function because a wave must be a function of x + vt or x − vt. Which one, if either, is correct, and why?

Accepted Answer

Ariel is correct because their equation can be rewritten as y = (x - 3.0t) which is a valid form for a pulse. This can be seen by rearranging the equation as follows: 11eb6adc_ee84_ebda_b0cf_27a9098c647c_TB8245_11 = y = 6.0xt - 9t² = (x - 3.0t)² This shows that the pulse is a function of x - vt, where v = 3.0 cm/s. Miranda's claim is incorrect because a pulse can be represented as a non-periodic function, so it does not need to be a function of x + vt or x - vt.

Question 13

Exhibit 16-1
The figure below shows a sine wave at one point of a string as a function of time.  Use the exhibit to answer the following question(s).
-Refer to Exhibit 16-1. Which of the graphs below shows a wave where the amplitude and the frequency are doubled?

Accepted Answer

Choice D shows a wave where the amplitude and frequency are doubled. The amplitude has increased from 1 to 2, and the frequency has increased from 1 cycle per second (or Hz) to 2 cycles per second (or Hz). The other graphs either show changes in amplitude or frequency, but not both.

Question 14

Earthquake waves are classified as P waves and S waves. Which of the following statements is true about these waves?

Accepted Answer

P waves are longitudinal, meaning that they propagate by compressing and expanding the material they travel through. S waves are transverse, meaning that they propagate by shearing the material they travel through.

Question 15

Exhibit 16-3
Four wave functions are given below.
I.y(x, t) = 5sin(4x - 20t + 4)
II.y(x, t) = 5sin(3x - 12t + 5)
III.y(x, t) = 5cos(4x + 24t + 6)
IV.y(x, t) = 14cos(2x - 8t + 3)
Use this exhibit to answer the following question(s).
-Refer to Exhibit 16-3. Rank the wave functions in order of the magnitude of the frequencies of the waves, from least to greatest.

Accepted Answer

The frequency of a wave is determined by the coefficient of the time variable in the wave function. The greater the coefficient, the higher the frequency. In this case, the wave functions with the greatest coefficients are IV and II, which have coefficients of -8 and -12, respectively. The wave functions with the smallest coefficients are I and III, which have coefficients of -20 and 24, respectively. Therefore, the correct answer is A.

Question 16

Which of the following is a solution to the wave equation,  ?

Accepted Answer

The answer of Which of the following is a solution...

Question 17

Exhibit 16-2
The figure below shows a sine wave on a string at one instant of time.  Use this exhibit to answer the following question(s).
-Refer to Exhibit 16-2. Which of the graphs below shows a wave where the wavelength is twice as large?

Accepted Answer

The answer of Exhibit 16-2
The figure below shows a sine...

Question 18

A piano wire of length 1.5 m vibrates so that one-half wavelength is contained on the string. If the frequency of vibration is 65 Hz, the amplitude of vibration is 3.0 mm, and the density is 15 g/m, how much energy is transmitted per second down the wire?

Accepted Answer

The answer of A piano wire of length 1.5 m...

Question 19

You are holding on to one end of a long string that is fastened to a rigid steel light pole. After producing a wave pulse that was 5 mm high and 4 cm wide, you want to produce a pulse that is 6 cm wide but still 5 mm high. You must move your hand up and down once,

Accepted Answer

The width of the pulse is determined by the time it takes for the hand to move up and down. To make a wider pulse while keeping the height the same, you need to move your hand up and down over a longer period of time, without changing the distance of the movement.

Question 20

Exhibit 16-2
The figure below shows a sine wave on a string at one instant of time.  Use this exhibit to answer the following question(s).
-Refer to Exhibit 16-2. Which of the graphs below shows a wave where the frequency and wave velocity are both doubled?

Accepted Answer

The answer of Exhibit 16-2
The figure below shows a sine...

Quiz 16: Wave Motion

To transmit four times as much energy per unit time along a string, you can

You are holding on to one end of a long string that is fastened to a rigid steel light pole. After producing a wave pulse that was 5 mm high and 4 cm wide, you want to produce a pulse that is 6 cm wide and 7 mm high. You must move your hand up and down once,

A student attaches a length of nylon fishing line to a fence post. She stretches it out and shakes the end of the rope in her hand back and forth to produce waves on the line. The most efficient way for her to increase the wavelength is to

Exhibit 16-1 The figure below shows a sine wave at one point of a string as a function of time. Use the exhibit to answer the following question(s) . -Refer to Exhibit 16-1. Which of the graphs below shows a wave where the amplitude and frequency are each reduced in half?

You are holding on to one end of a long string that is fastened to a rigid steel light pole. After producing a wave pulse that was 5 mm high and 4 cm wide, you want to produce a pulse that is 4 cm wide but 7 mm high. You must move your hand up and down once,

Suppose that you were selected for a "Survivor"-type TV show. To help keep your group connected, you suggest that long vines can be tied together and used to transmit signals in cases of emergency. To get the signals to travel faster, you should

The wave equation is written down in an exam as From dimensional considerations we see that

Find the period of a wave of 100-m wavelength in deep water where .

Ariel claims that a pulse is described by the equation where x and y are measured in cm and t in s. Miranda says that it is not possible to represent a pulse with this function because a wave must be a function of x + vt or x − vt. Which one, if either, is correct, and why?

Exhibit 16-1 The figure below shows a sine wave at one point of a string as a function of time. Use the exhibit to answer the following question(s) . -Refer to Exhibit 16-1. Which of the graphs below shows a wave where the amplitude and the frequency are doubled?

Earthquake waves are classified as P waves and S waves. Which of the following statements is true about these waves?

Which of the following is a solution to the wave equation, ?

Exhibit 16-2 The figure below shows a sine wave on a string at one instant of time. Use this exhibit to answer the following question(s) . -Refer to Exhibit 16-2. Which of the graphs below shows a wave where the wavelength is twice as large?

A piano wire of length 1.5 m vibrates so that one-half wavelength is contained on the string. If the frequency of vibration is 65 Hz, the amplitude of vibration is 3.0 mm, and the density is 15 g/m, how much energy is transmitted per second down the wire?

You are holding on to one end of a long string that is fastened to a rigid steel light pole. After producing a wave pulse that was 5 mm high and 4 cm wide, you want to produce a pulse that is 6 cm wide but still 5 mm high. You must move your hand up and down once,

Exhibit 16-2 The figure below shows a sine wave on a string at one instant of time. Use this exhibit to answer the following question(s) . -Refer to Exhibit 16-2. Which of the graphs below shows a wave where the frequency and wave velocity are both doubled?