Question

15 beats are heard in 5 seconds when a piano key and a tuning fork of slightly higher frequency (440 Hz) are struck at the same time. What is the frequency of the sound emitted by the piano key?

Answer 1

437Hz

Step-by-step explanation:

if two sound waves have a little difference in frequencies
`f_(a)` and
`f_(a)<f_(b)` interfere, the resulting sound wave produces a beat.

Given:

`f_(a)=440Hz`

`f_(b)=frequency\ of\ the\ sound\ emitted by\ the\ piano\ key`

`f_(beat)=frequency\ of\ beat`

where

`f_(beat)=(number\ of\ beat)/(time)`

`f_(beat)=(15beats)/(5)=3Hz`

`f_(beat)=f_(a)-f_(b)`

`f_(b)=f_(a)-f_(beat)` = 440Hz - 3Hz = 437Hz