**PHY
1150**

__Chapter 14; Waves and Sound__

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**D14.1 What is the wavelength of a 50 Hz wave when the wave
speed is 340 m/s ?**

**
= ^{v} / _{f}**

**
**

T = v

T = 540 N

**
**

**
**

**
**

**f _{1} = 440 Hz**

_{1}
= (^{1}/_{2}) L

_{n}
= (^{1}/_{n}) _{1}

or

f_{n} = n f_{1}

**f _{1} = 440 Hz**

f

f

f

f

f

f

f

**etc
f _{45} 20
000 Hz will be near or beyond the range of hearing.**

**D14.6 A guitar string 0.70 m long is tuned to play A at 440 Hz whe
its full length vibrates. Where should a finger be placed in order to play C
at 524 Hz?**

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

/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.

**
**

** D14.7 A demonstration is carried out with the apparatus
shown here. A mass is suspended on one end of a string (so the tension in the
string is the weight of the mas, mg). The string is then run over a pulley and
attached to a small-amplitude 60-Hz oscillator. As additional masses are placed
on the end, standing waves appear. The distance between pulley and oscillator
is 2.4 m. That amoun of string has a mass of 45 g. How much mass is supported
when the standing wave -- with three "loops" -- shown in the diagram
is produced?**

**/2
= 2.4 m / 3 = 0.80 m**

**
= 1.6 m
f = 60 Hz = 60 (**

v = f = (60/s) (1.6 m) = 96 m/s

T = v

T = v

T = m g

m = T/g = (172.8 N ) / (9.8 m/s

m = 17.6 kg

**D14.8 With the string and arrangement shown in the problem
above, what hanging mass is necessary to produce a standing wave of five "loops"
if the distance from pulley to oscillator remains at 2.4 m?**

**
= 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 use in the lab -- has (3/4) of a wavelength.

**
**

** D14.10 A ringing tuning fork is held above a tube in a
Physics experiment. The tube is filled with water whose level can be altered
easily, thus changing the length of the column of air below the tuning fork.
As the water level is lowered, lengthening the column of air, an increase in
loudness is noted when the water is 0.120, 0.360, and 0.600 m from the top of
the tube. Assume the speed of sound in air is 345 m/s. What is the frequency
of the tuning fork?**

**This one should be (very) familar!**

= 0.480 m

v = f

**
**

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

**
**

** D14.12 A train whistle sounds at 500 Hz. What frequency
is heard by a stationary observer when the train approaches at 25 m/s? When
it moves away at 25 m/s?**

**What frequency is heard by a moving observer as she approaches
the stationary train at 25 m/s? As she moves away from the stationary train
at 25 m/s? **

**Take the speed of sound in air to be 340 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 Hz. 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) 2005, Doug Davis; all rights reserved