Two sound waves have equal displacement amplitudes, but one has twice the frequency of the other. A) Which has

Question

the greater pressure amplitude and by what factor is it greater? B) What is the ratio of their intensities?

Please show work! Thank you*

Answer 1

See the ref. The sound pressure is proportional to particle velocity. Velocity is proportional to the product of amplitude and frequency. Thus the higher frequency sound has twice the pressure of the lower one.
Intensity is the product of particle velocity and pressure, therefore it increases as the square of the pressure. The higher frequency sound has four times the intensity of the lower one.

Answer 2

Haven't done this for a long time, but here's what I remember. Based on summing the trig expressions for the two frequencies, superposed, For two frequencies, f beat = (f1 - f2) (v-1) and v beat frequency = 1 hz (v+1) and v beat frequency = 1 hz, 180 degrees out of phase with other sideband Thus, the sideband superpositions cancel and there is no resultant beat. hth