Question

What beat frequencies result if a piano hammer hits three strings that emit frequencies of 127.8, 128.1, and 123.8 Hz?

Short answer

The beat frequencies are 0.3 beat/s, 0.2 beat/s, 0.5 beat/s.

Step-by-step solution

Given Data

The frequency of the first is\[{f_1} = 127.8\;Hz\].

The frequency of the second is\[{f_2} = 128.1\;Hz\].

The frequency of the third is \[{f_3} = 123.8\;Hz\].

Calculation of the beat frequency

The beat frequency is,

\[f = \left| {{f_1} - {f_2}} \right|\]

Plugging the values,

\[\begin{aligned}{f_{12}} = \left| {127.8 - 128.1} \right|\\ = 0.3\;beats/s\end{aligned}\]

\[\begin{aligned}{f_{13}} = \left| {128.3 - 127.8} \right|\\ = 0.5\;beats/s\end{aligned}\]

\[\begin{aligned}{f_{23}} = \left| {128.3 - 128.1} \right|\\ = 0.2\;beats/s\end{aligned}\]

Therefore the frequency of first is 0.3 beat/s, second is 0.2 beat/s and the third is 0.5 beat/s.