A point source that is stationary on an x axis emits a sinusoidal sound wave at

Question

A point source that is stationary on an x axis emits a sinusoidal sound wave at a frequency of 747 Hz and speed 344 m/s. The wave travels radially outward from the source, causing air molecules to oscillate radially inward and outward. Let us define a wavefront as a line that connects points where the air molecules have the maximum, radially outward displacement. At any given instant, the wavefronts are concentric circles that are centered on the source. (a) Along x, what is the adjacent wavefront separation? Next, the source moves along x at a speed of 137 m/s. Along x, what are the wavefront separations (b) in front of and (c) behind the source?

Explanation / Answer

(a) Adjacent wavefront separation, x = = c/f = 344 / 747 = 0.46 m

(b) Due to Doppler effect, x = front = [(c - vs) / c] = [(344 - 137) / 344] * 0.46 = 0.28 m

(c) Due to Doppler effect, x = behind = [(c + vs) / c] = [(344 + 137) / 344] * 0.46 = 0.64 m

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