Question

Tuning a piano to tune middle c on a piano, a tuner hits the key and at the same time sounds a 261 hz tuning fork. if the turner hears 3 beats per second, what are the possible frequencies of the piano key?

Answer 1

This question deals with the physics of resonance and sound. The possible frequency of the pano key is 258hz.

How to compute the variation in frequency

The beat of a frequency is the difference (an absolute value) in the frequencies produced by the two waves.

Beat per second equals |f1 - f2| Where

ft = Frequency of the Tunning fork and

fp= Frequency of the Piano Key

Hence

3 =  261 - fp

Solving for fp,

fp = 261-3

= 258hz

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