university physics mastering physics ch15

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Chapter 15 Assignment

Due: 11:00pm on Wednesday, January 25, 2012

Note: To understand how points are aw arded, read your instructor's Grading Policy.

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Exercise 15.1

The speed of sound in air at 20 is 344 .

Part A

What is the wavelength of a sound wave with a frequency of 784 , corresponding to the note

on a piano?

ANSWER: = 0.439

Correct

Part B

How many milliseconds does each vibration take?

ANSWER: = 1.28

Correct

Part C

What is the wavelength of a sound wave one octave higher than the note in part A?

ANSWER: = 0.219

Correct

Exercise 15.16

A 1.70- string of weight 1.22 is tied to the ceiling at its upper end, and the lower end supports

a weight . When you pluck the string slightly, the waves traveling up the string obey the

equation

Part A

How much time does it take a pulse to travel the full length of the string?

ANSWER: = 0.11

Correct

[ Print ]



Part B

What is the weight ?

ANSWER: = 18

Correct

Part C

How many wavelengths are on the string at any instant of time?

ANSWER: = 47

Correct

Part D

What is the equation for waves traveling down the string?

ANSWER:

Correct

Exercise 15.20

A piano wire with mass 3.50 and length 83.0 is stretched with a tension of 29.0 . A wave

with frequency 120 and amplitude 1.30 travels along the wire.

Part A

Calculate the average power carried by the wave.

ANSWER: = 0.168

Correct

Part B

What happens to the average power if the wave amplitude is halved?

ANSWER: = 4.20×10−2

Correct



Exercise 15.28: Interference of Triangular Pulses

Two triangular wave pulses are traveling toward each other on a stretched string as shown in thefigure . Each pulse is identical to the otherand travels at 2.00 . The leading

edges of the pulses are 1.00 apart at

= 0.

Part A

Sketch the shape of the string at = 0.250 .

ANSWER:

View Correct

Part B


ANSWER:

View Correct

Part C




ANSWER:

View Correct

Part D


ANSWER:

View Correct

Part E


ANSWER:

View Correct

Exercise 15.34

Adjacent antinodes of a standing wave on a string are 15.0 apart. A particle at an antinode

oscillates in simple harmonic motion with amplitude 0.850 and period 0.0750 . The string lies



along the +x-axis and is fixed at .

Part A

How far apart are the adjacent nodes?

ANSWER: = 15.0

Correct

Part B

What is the wavelength of the two traveling waves that form this pattern?

ANSWER: = 30.0

Correct

Part C

What is the amplitude of the two traveling waves that form this pattern?

ANSWER: = 0.425

Correct

Part D

What is the speed of the two traveling waves that form this pattern?

ANSWER: = 4.00

Correct

Part E

Find the maximum and minimum transverse speeds of a point at an antinode.

Enter your answers numerically separated by a comma.

ANSWER: , = 0.712,0

Correct

Part F

What is the shortest distance along the string between a node and an antinode?

ANSWER: = 7.50

Correct

Exercise 15.40



A piano tuner stretches a steel piano wire with a tension of 800 . The steel wire is 0.400 long

and has a mass of 3.00 .

Part A

What is the frequency of its fundamental mode of vibration?

ANSWER: = 408

Correct

Part B

What is the nurmber of the highest hamonic that could be heard by a person who is capable ofhearing frequencies up to 10000 Hz?

ANSWER: = 24

Correct

Problem 15.50

A transverse wave on a rope is given by

.

Part A

Find the amplitude.

ANSWER: = 0.750

Correct

Part B

Find the period.

ANSWER: = 8.00×10−3

Correct

Part C

Find the frequency.

ANSWER: = 125

Correct

Part D



Find the wavelength.

ANSWER: = 5.00

Correct

Part E

Find the speed of propagation.

ANSWER: = 6.25

Correct

Part F

Is the wave traveling in the x- or x-direction?

ANSWER: x-direction

x-direction

Correct

Part G

The mass per unit length of the rope is 0.0500 . Find the tension.

ANSWER: = 1.95

Correct

Part H

Find the average power of this wave.

ANSWER: = 5.42

Correct

Problem 15.56

A 4.91- , 0.740- wire is used to support two uniform 239- posts of equal length (the figure ).

Assume that the wire is essentially horizontal and that the speed of sound is 344 . A strong

wind is blowing, causing the wire to vibrate in its 7th overtone.



Part A

What is the frequency of the sound this wire produces?

ANSWER: = 18.5

Correct

Part B

What is the wavelength of the sound this wire produces?

ANSWER: = 18.6

Correct

Problem 15.61: Waves of Arbitrary Shape

Part A

Explain why any wave described by a function of the form moves in the

-direction with speed .

Essay answers are limited to about 500 words (3800 characters maximum, includingspaces).

ANSWER: My Answer:Because its speed is v, the wave pulse travels to the right a distance vt in a timet. If a wave moves in the positive x direction with speed v, then at time t it will beshown by y = f(x − vt).

Part B

Show that satisfies the wave equation, no matter what the functional form



of . To do this, write , where . Then, to take partial derivatives of

, use the chain rule:

Essay answers are limited to about 500 words (3800 characters maximum, includingspaces).

ANSWER: My Answer:df/dx = (df/du)(du/dx) = df/du d 2̂f/dx 2̂ = d(df/du)/du(du/dx) = d 2̂f/du 2̂ df/dt =(df/du)(du/dt) = (df/du)(-v) d 2̂f/dt 2̂ = (-v)d(df/du)/du(du/dt) = v̂ 2d 2̂f/du 2̂Comparing: d 2̂f/dx 2̂ = (1/v̂ 2)d 2̂f/dt 2̂

Part C

A wave pulse is described by the function , where , , and are all

positive constants. What is the speed of this wave?

Express your answer in terms of the variables , , .

ANSWER:

=

Correct

Problem 15.68

A vibrating string 52.0 long is under a tension of 0.990 . The results from five successive

stroboscopic pictures are shown in the figure . The strobe rate is set at 5000 flashes per minute,and observations reveal that the maximumdisplacement occurred at flashes 1 and 5with no other maxima in between.

Part A

Find the period for the traveling waves on this string.



ANSWER: = 9.60×10−2

Correct

Part B

Find the frequency for the traveling waves on this string.

ANSWER: = 10.4

Correct

Part C

Find the wavelength for the traveling waves on this string.

ANSWER: = 0.520

Correct

Part D

In what harmonic is the string vibrating?

ANSWER: = 2

Correct

Part E

What is the speed of the traveling waves on the string?

ANSWER: = 5.42

Correct

Part F

How fast is point P moving when the string is in position 1?

ANSWER: = 0

Correct

Part G

How fast is point P moving when the string is in position 3?

ANSWER: = 0.980

Correct



Part H

What is the mass of this string?

ANSWER: = 17.5

Correct

Problem 15.85: Out of Tune

The B-string of a guitar is made of steel (density ), is 63.5 cm long, and has diameter

0.406 mm. The fundamental frequency is f = 247.0 Hz.

Part A

Find the string tension.

ANSWER: = 99.4

Correct

Part B

If the tension is changed by a small amount , the frequency changes by a small

amount given by . The string is tuned as in part (a) when its temperature is

. Strenuous playing can make the temperature of the string rise, changing its vibration

frequency. Find if the temperature of the string rises to . The steel string has a

Young's modulus of and a coefficient of linear expansion of .

Assume that the temperature of the body of the guitar remains constant.

ANSWER: = -4.20

Correct

Part C

Will the vibration frequency rise or fall?

ANSWER:rise

fall

Correct

Score Summary:

Your score on this assignment is 100%.You received 22 out of a possible total of 22 points.

university physics mastering physics ch15

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