# 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.

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#### 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.