Physics 102 Homework #2
Due Noon, Tuesday, February 2, 2010
Submit your paper in the bin in the hall adjacent to Park 354.
Revised, January 24:
Corrected reading assignment (§16.7 added)
Revised, February 1:
Problem 12: Answer in text is wrong. Correct answer given at the end of this assignment.
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Reading:
This week: Knight, Jones, & Field § 16.1-16.4, 16.6-16.7
Next week: Knight, Jones, & Field § 17 and § 28.1
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Problems: Four problems will be chosen for grading. They will be selected at random from
among those problems indicated with asterisks. You do not need to submit solutions to the
non-asterisk problems.
“KJF” means your textbook, College Physics, by Knight, Jones, and Field. The problems
in this homework are deliberately presented in a different order than given in the textbook.
For problems involving sound in air, use a speed of 343 m/s unless some other speed is
specified. For problems involving light, radio waves, etc., use a speed of 3.0 × 108 m/s.
1. Weekly metric prefix review. Answers are given at the end of this assignment. As
a reminder, you are expected to know the following metric prefixes. They will be
explicitly tested on the first exam.
Prefix
tera
giga
mega
kilo
Abbreviation
T
G
M
k
Multiplier
1012
109
106
103
Prefix
milli
micro
nano
Abbreviation
m
µ
n
Multiplier
10−3
10−6
10−9
(a) What is 10 km in mm?
(b) What is 100 µm
ns in
m
s?
(c) How far does light travel in 1 ns? Give your answer in cm.
(d) How many 2 Mbyte computer picture files can you fit onto a 350 Gbyte disk?
2. KJF Problem 16.1.
3. KJF Problem 16.9.
4. * KJF Problem 16.10.
5. * KJF Problem 16.12.
6. * KJF Problem 16.16. Add part (c): draw a picture of the standing wave described
in the first two sentences of this problem. You might want to do this part first.
Continued on the next page....
hh
(( X
X
((
(h
hhh XX
7. * The world’s largest pipe organ is the Wanamaker Organ in the (
Wanamaker’s
Hecht’s
(h
hhhh(((
(
(
h
(
Lord
&
Taylor
Macy’s
store
in
Center
City
Philadelphia,
across
the
street
from
City
hh
((
h
Hall. Be sure to see it while you’re living in the area. It consists of more than 28,000
organ pipes, the longest of which is 32 feet long and the shortest of which 1/4 inch long.
What are the fundamental frequencies of the longest and shortest pipes? Assume the
longest pipe is open on both ends, and that the shortest pipe is open on one end and
closed on the other end. For conversion between imperial and metric units, consult
the inside front cover of your text, or use the internet. (Try typing the following into
Google: “32 feet in meters”).
8. KJF Problem 16.43.
9. KJF Problem 16.49.
10. KJF Problem 16.52. (Answer is given at the end of this assignment.)
11. KJF Problem 16.35.
12. KJF Problem 16.71. (Answer in the text is incorrect; the correct answer is given at
the end of this assignment.)
13. KJF Problem 16.59. Assume the sounds emitted by the two speakers are synchronized
with one another (e.g., they emit wave crests at the same time).
14. * The figure below shows two speakers, A and B, which are emitting identical,
synchronized sound waves at 830 Hz. A person standing at point C hears a relatively
loud sound. She then starts walking toward point D, and she notices that the sound
gets quieter, reaching a minimum when she arrives at D. The distance from speaker
A to D is 2.50 m. The distance from speaker B to D is 2.30 m. It is a cold day, and
the speed of sound is not 343 m/s.
(a) From the information given above, what is the wavelength of the sound?
(b) From the information given above, what is the speed of the sound?
(c) She remains at point D, and someone slowly increases the frequency of the sound
emitted by the two speakers. It starts to sound louder to her. What is the first
frequency at which the sound intensity goes through a maximum?
A
C
B
D
Continued on the next page....
15. * The sound produced by the speaker in the drawing below has a frequency of
12 000 Hz and arrives at the microphone via two different paths. The sound waves
simultaneously travel through the left tube, sxm, which has a fixed length, and the
right tube, sym, the length of which can be changed by moving the sliding section
(similar to a trombone). The tubes are filled with a gas, but it is not air at standard
pressure and temperature.
The sound waves traveling via the two paths combine at the microphone and interfere.
As the length of path sym is changed, the sound loudness detected by the microphone
changes. When the sliding section is pulled out by 0.020 m the loudness changes from
a maximum to a minimum. Based on this measurement, what is the speed of sound
in the gas in the tube?
Hint #1: first find the wavelength of the sound, λ, then use it to calculate v.
Hint #2: think carefully about how the distance traveled by the sound wave traveling
through the sliding section changes when it is pulled out by 0.020 m. This is an easy
place to make a factor-of-2 error.
speaker
S
sliding section
X
Y
M
microphone
16. * An AM radio station broadcasts at 610 kHz. It transmits a signal simultaneously
from two antennas, one of which is 245 m north of the other. The antennas are
synchronized: they transmit precisely the same signal with the same power. Radio
signals travel at the speed of light, 3.0 × 108 m/s.
(a) In what directions will a strong radio signal be detected? In what directions will
the radio signal be weak or undetectable? (Your answers should be directions
like “north” or “east”.)
(b) How would the answer change if the north transmitter was precisely out of
phase with the south transmitter, i.e., if it emitted wave crests when the south
transmitter emitted troughs?
Answer to selected problems:
(1) 1.0 × 107 mm, 1.0 × 105 ms , 30.0 cm, 175,000. (10) open-open, 1.32 m. (12) 0.20 ms .