1. A tuning fork with a frequency of 440 Hz is

*played*simultaneously with a fork with a frequency of 437 Hz. How many beats will be heard over a period of 10 seconds?
Answer:

**30 beats**
The beat frequency will be 3 Hz; thus in 10 seconds, there should
be 30 beats.

2. Why don't we hear beats when different keys on the
piano are played at the same time?

Answer:

Our ears can only detect beats if the two interfering sound waves have a difference in frequency of 7 Hz or less. No two keys on the piano are that similar in frequency.

3. Suppose you are standing on the passenger-loading
platform of the commuter railway line. As the commuter train
approaches the station, it gradually slows down. During this
process of slowing down, the engineer sounds the horn at a
constant frequency of 300 Hz. What pitch or changes in pitch
will you perceive as the train approaches you on the loading
platform?

Answer:

This is a tough question! First you know that the pitch which you
hear will be greater than 300 Hz since the sound source is
approaching you. But once stopped, the pitch will be 300 Hz exactly.
So the pitch must be gradually decreasing from above 300 Hz to 300 Hz
during the slowing down process.

4. The sound produced by blowing over the top of a
partially filled soda pop bottle is the result of the air
column inside of the bottle vibrating at its natural
frequency. The actual frequency of vibration is inversely
proportional to the wavelength of the sound; and thus, the
frequency of vibration is inversely proportional to the
length of air inside the bottle. Express your understanding
of this resonance phenomenon by filling in the following
table.

Answer:

The speed of wave is not dependent upon wave properties such as
wavelength and frequency. Thus, the speed of the sound wave is 340
m/s for each of the four bottles.

For Bottle C, the frequency can be determined from knowledge of
the speed and the wavelength using the wave equation: v = f •
where
is the
wavelength. First, rearrange the equation. Then substitute and solve
as shown below.

f = v / = (340 m/s) / (0.64 m) =531 Hz

For all four bottles, the length of the air column inside the
bottle is one-fourth the wavelength of the wave. This is evident when
looking at the length - wavelength relationships for Bottles A and B.
Put in equation form: L = 0.25 •
where is the
wavelength. For Bottle C:

L = 0.25 • = 0.25 • (0.64 m) =0.16 m

For Bottle D, the determination of the wavelength demands that the
L = 0.25 •
equation be rearranged.

= 4 • L = 4 • 0.20 m =

**0.80 m**