Question

problem 24. Two overlapping, harmonic waves have the same frequency, speed, and amplitude (5.0 cm). They travel in the same direction in the same medium. They differ in phase by ?/2. What is the amplitude of the superposed wave?

problem 28. A flutist assembles her flute in a room where the speed of sound is 342 m/s. She is in perfect tune with a 440 Hz tuning fork. A few minutes later, the room has warmed and the speed of sound is 346 m/s. What is the beat frequency between the flute and tuning fork?

Answer 1

Problem 24

The amplitude of a superposed wave made up of two similar waves with differing phase constants is

where is the phase difference.

Substituting the given values, we get

Problem 28

The beat frequency will be zero, as the frequency of the driving source, the flute, will remain the same. Since the speed of sound has changed, the wavelength of the emitted sound will change. However, the frequency will depend solely on the driver. As beat frequency depends on the difference of frequencies between two sources, in this case, it will be zero.