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In certain ranges of a piano keyboard, more than one string istuned to the same note to provide extra loudness. For example, thenote at 1.10 x 102 Hz has two strings at this frequency.If one string slips from its normal tension of 6.00 x102 N to 5.40 x 102 N, what beatfrequency is heard when the hammer strikes the two stringssimultaneously?

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Answer:

The beat frequency is 5.5 Hz.

Explanation:

f = 110 Hz, T = 600 N , T' = 540 N

let the frequency is f'.

[tex]\frac{f'}{f}=\sqrt\frac{T'}{T}\\\\\frac{f'}{f}=\sqrt\frac{540}{600}\\\\\frac{f'}{f}=0.95\\\\f'= 104.5 Hz[/tex]

So, the beat frequency is f - f' = 110 - 104.5 = 5.5 Hz

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