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?
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?
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.
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