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Two sound waves are emitted; show equation of the sum and beat frequency of waves

Two sound waves are emitted: y1, with frequency f1, and y2, with frequency f2, with other constants identical, as expressed below. Distances in meters, times in seconds, and angles in radians:
(1) y1 = .02 sin(8 Pi x - 108 Pi t) (2) y2= .02 sin (8 Pi x - 100 Pi t)

The two waves add to produce the sound perceived by a listener.

PART a. Show y, the equation of the sum, y1 + y2, of the two waves.

PART b. Find the beat frequency of the combined waves.

Solution Preview

When two slightly different frequencies are propagated simultaneously, interference occurs between them and they combine together to produce a "beat note" whose frequency is fb = .5 (f2 - f1). Guitars are often tuned by using this phenomenon. If one string sounds a certain frequency, then another string's tension is adjusted until their beat note frequency becomes zero; then the two strings ...

Solution Summary

The two sound waves which are emitted are determined. Sound waves perceived by a listener are determined. In a step by step solution, the answers are derived using the formulas presented.