PHY 1150
Chapter 16; Waves and Sound
16.2, 12, 14a, 14b, 16, 17, 21, 22, 28, 32, 49, 54

16.2

v = f

= v/f

16.12

T = v2 (m/L) = (30 m/s)2 (0.6 kg/m)
T = 540 N

16.14a

16.14 b

16.16 f1 = 440 Hz
fn = n f1

f2 = 880 Hz
f3 = 1 760 Hz
f4 = 3 520 Hz
f5 = 7 040 Hz
f6 = 14 080 Hz
f7 = 28 160 Hz will be ultrasonic, and cannot be heard

16.17 The velocity of the wave on the string is given by

v = f
/2 = 0.70 m
= 1.4 m
v = (440 Hz) (1.4 m)
v = 616 m/s

/2 = 0.588 m
That is, your finger should be placed so the string that vibrates is 0.588 m (or 0.59 m) long.

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 = v
2 (m/L)

T = v
2 (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.
(3/4)2 = 1.0 m
2 = 1.33 m

16.28 This one should be (very) familar!

(1/2) = 0.600 m - 0.360 m = 0.360 m - 0.120 m = 0.240 m
= 0.480 m
v = f

16.32

v = [331 + (0.60)(42)] m/s

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
v
obs = 0
v
s = ? (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.

340 = (1.0036)(340 - v
s) = 341.236 &endash; 1.0036 vs
1.0036 v
s = 1.236

340 = (0.9964)(340 + v
s) = 338.764 + 0.9964 vs
0.9964 v
s = 1.236

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.