PHY
1150
Chapter 16; Waves
and Sound
16.2, 12, 14a, 14b, 16, 17,
21, 22, 28, 32, 49, 54
PHY
1150
Chapter 16; Waves
and Sound
16.2, 12, 14a, 14b, 16, 17,
21, 22, 28, 32, 49, 54
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16.2
= v/f
16.12
16.14a
16.14 b
16.17 The velocity of the wave on the
string is given by
/2
= 0.70 m
= 1.4 m
/2
= 0.588 m
16.21 With the string and arrangement of Figure 16.49, what mass is
necessary to produce a standing wave of five loops if the distance
from pulley to oscillator is increased to 2.8 m?
/2
= 2.8 m/5 = 0.56 m
= 1.12 m
f = 60 Hz = 60
(1/s)
v = f
= (60/s) (1.12 m) = 67.2 m/s
T =
v2
(m/L)
T =
v2
(m/L) = (67.2
m/s)2
(0.01875 kg/m) = 84.67 N
T = m g
m = 8.64 kg
16.22 An organ pipe open at one end and closed at the other is 1.0 m
long. What is its fundamental frequency? Its first overtone
frequency?
1
= 4.0 m
v = f
The next overtone is such an open pipe -- exactly like the resonance tubes we used in the lab -- has (3/4) of a wavelength.
2
= 1.0 m2
= 1.33 m
16.28 This one should be (very) familar!
= 0.600 m - 0.360 m = 0.360 m - 0.120 m = 0.240 m
= 0.480 m
16.32
v = [331 + 25] m/s
v = 356 m/s
16.49
f ' = (500 Hz) (1.079) = 540 Hz
f ' = (500 Hz) (0.932) = 466 Hz
f' = (500 Hz) (1.074) = 537 Hz
f' = (500 Hz) (0.926) = 463 Hz
16.54
f = 550 Hz
v = 340 m/s
vobs
= 0
vs = ? (we are
looking for the velocity of the
source).
A beat frequency of 2 Hz means the frequency heard from the moving train's horn must be different from 550 Hz by 2. Therefore, for the approaching train, the frequency heard must be 552 Hz, and for the train going away, the frequency heard must be 548 Hz.
Remember, however, the "beat frequency of 2 Hz" is stated to only one significant figure. We are unjustified in keeping three significant figures in our answers.
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(c) 2000, Doug Davis; all rights reserved