Answered

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 :

Debel

Answer:

437Hz

Explanation:

if two sound waves have a little difference in frequencies [tex]f_{a}[/tex]     and [tex]f_{a}<f_{b}[/tex]       interfere, the resulting sound wave produces a beat.

Given:

[tex]f_{a}=440Hz[/tex]

 [tex]f_{b}=frequency\ of\ the\ sound\ emitted by\ the\ piano\ key[/tex]

[tex]f_{beat}=frequency\ of\ beat[/tex]

where

[tex]f_{beat}=\frac{number\ of\ beat}{time} [/tex]

[tex]f_{beat}=\frac{15beats}{5}=3Hz[/tex]

[tex]f_{beat}=f_{a}-f_{b}[/tex]

[tex]f_{b}=f_{a}-f_{beat}[/tex] = 440Hz - 3Hz = 437Hz

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