18. Waves & Sound

Two sinusoidal waves with amplitudes $4.5\mathrm{cm}$ and $3.0\mathrm{cm},$ respectively, move toward each other on a string and experience superposition. As they move past each other, the displacement of the string from equilibrium is complicated. Considering all positions on the string where the waves are overlapping, what are the largest and smallest magnitudes of the displacement of the string?

Suppose you are listening to two tones, one of 50Hz, and the other of 10,000 Hz. If the sources of these tones are equal in intensity at your location, which do you perceive to have a higher sound intensity level (in dB), and by what factor?

You are standing $3.0\mathrm{m}$ from one speaker and $2.5\mathrm{m}$ from another. Both are emitting identical 680Hz tones in phase. What best describes what you would observe? Use $340\text{ m/s}$ for the speed of sound.

Two speakers (A and B) lie on the y-axis, $4.0\mathrm{m}$ apart. They emit exactly the same 280 Hz tone in phase with each other. You start right at speaker A and walk in the x-direction. How far from speaker A do you first hear a minimum in sound intensity? Assume the speed of sound in this room is $340\text{ m/s}.$