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Two sources of sound are producing waves of frequency η1 and η2 where (η1-η2) is small,show mathematically that the beat frequency is (η1-η2)
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Asked by aniket 20th March 2017, 5:49 PM
Answered by Expert
Answer:

begin mathsize 12px style Hi space Aniket comma
The space two space sources space are space of space frequency space straight eta subscript 1 and space straight eta subscript 2 space respectively.
So comma space their space amplitudes space are space cos open parentheses 2 πη subscript 1 straight t close parentheses space and space cos left parenthesis 2 πη subscript 2 straight t right parenthesis
Therefore comma space the space resultant space amplitude space is
space cos open parentheses 2 πη subscript 1 straight t close parentheses plus cos left parenthesis 2 πη subscript 2 straight t right parenthesis equals 2 cos open parentheses 2 straight pi fraction numerator straight eta subscript 1 plus straight eta subscript 2 over denominator 2 end fraction straight t close parentheses cos open parentheses 2 straight pi fraction numerator straight eta subscript 1 minus straight eta subscript 2 over denominator 2 end fraction straight t close parentheses end style

Here, the frequency η1 - η2 is the beat frequency.

Answered by Expert 20th March 2017, 5:59 PM
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