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

Answer:

437Hz

Explanation:

if two sound waves have a little difference in frequencies $f_{a}$     and $f_{a}$       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

$f_{beat}=\frac{number\ of\ beat}{time}$

$f_{beat}=\frac{15beats}{5}=3Hz$

$f_{beat}=f_{a}-f_{b}$

$f_{b}=f_{a}-f_{beat}$ = 440Hz - 3Hz = 437Hz