Download - University Physics Mastering Physics Ch15
5/16/12 MasteringPhysics: MasteringPhysics: Scores
1/12session.masteringphysics.com/myct/scores
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.
[Sw itch to Standard Assignment View ]
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 ]
5/16/12 MasteringPhysics: MasteringPhysics: Scores
2/12session.masteringphysics.com/myct/scores
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
5/16/12 MasteringPhysics: MasteringPhysics: Scores
3/12session.masteringphysics.com/myct/scores
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
Sketch the shape of the string at = 0.500 .
ANSWER:
View Correct
Part C
5/16/12 MasteringPhysics: MasteringPhysics: Scores
4/12session.masteringphysics.com/myct/scores
Sketch the shape of the string at = 0.750 .
ANSWER:
View Correct
Part D
Sketch the shape of the string at = 1.000 .
ANSWER:
View Correct
Part E
Sketch the shape of the string at = 1.250 .
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
5/16/12 MasteringPhysics: MasteringPhysics: Scores
5/12session.masteringphysics.com/myct/scores
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
5/16/12 MasteringPhysics: MasteringPhysics: Scores
6/12session.masteringphysics.com/myct/scores
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
5/16/12 MasteringPhysics: MasteringPhysics: Scores
7/12session.masteringphysics.com/myct/scores
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.
5/16/12 MasteringPhysics: MasteringPhysics: Scores
8/12session.masteringphysics.com/myct/scores
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
5/16/12 MasteringPhysics: MasteringPhysics: Scores
9/12session.masteringphysics.com/myct/scores
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.
5/16/12 MasteringPhysics: MasteringPhysics: Scores
10/12session.masteringphysics.com/myct/scores
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
5/16/12 MasteringPhysics: MasteringPhysics: Scores
11/12session.masteringphysics.com/myct/scores
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.
5/16/12 MasteringPhysics: MasteringPhysics: Scores
12/12session.masteringphysics.com/myct/scores