**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
**

**
**

T = v

T = 540 N

**
**

**
**

16.16 f

f

f

f

f

f

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.

**
**

**
= 1.12 m
f = 60 Hz = 60
(**

v = f = (60/s) (1.12 m) = 67.2 m/s

T = v

T = v

T = m g

m = 8.64 kg

**
**

_{1}**
= 4.0 m
v = f
**

The next overtone is such an open pipe --exactlylike the resonance tubes we used in the lab -- has (3/4) of a wavelength.

**
**

= 0.480 m

v = f

**
**

**v = [331 + 25] m/s
v = 356 m/s**

**
**

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

**
**

**f = 550 Hz
v = 340 m/s
v**

v

**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

1.0036 v

340 = (0.9964)(340 + v

0.9964 v

**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