Question

The middle-C hammer of a piano hits two strings, producing beats of 1.55 Hz. One of the strings is turned to 230.00 Hz. What frequencies (in Hz) could the other string have? (Answer to the nearest 0.1 Hz.) Hz (lower possible frequency) = Hz (higher possible frequency) =

Answer 1

The beat frequency can be calculated with the formula below:

$f_{beat}=|f_1-f_2|$

If the beat frequency is 1.55 Hz and one of the frequencies is 230 Hz, we have:

$\begin{gathered} 1.55=|230-f_2|\\ \\ \begin{cases}230-f_2=1.55\rightarrow f_2=228.45\text{ Hz}{} \\ 230-f_2=-1.55\rightarrow f_2=231.55\text{ Hz}{}\end{cases} \end{gathered}$

Therefore the lower frequency is 228.4 Hz and the higher frequency is 231.6 Hz.