Q41PE - College Physics (Urone)

Question

A piano tuner hears a beat every 2.00 s when listening to a 264.0 Hz tuning fork and a single piano string. What are the two possible frequencies of the string?

Step-by-Step Solution

Answer

The possible frequencies are 263.6 Hz and 264.5 Hz.

Step 1: Given Data

The frequency of the fork is f = 264.0 Hz.

The beat frequency is 1 per 2 sec.

Step 2: Frequency of beats

The frequency of beats is given by,

\(f = \left| {{f_1} - {f_2}} \right|\)

Here f1 is the frequency of the string and f2 is the frequency of the fork.

Step 3: Calculation of the unknown frequency

The beat frequency is,

\(f = \left| {{f_1} - {f_2}} \right|\) 

Plugging the values,

\(\begin{aligned}\frac{1}{2} = \left| {264 - {f_2}} \right|\\264 - {f_2} =   \pm 0.5\end{aligned}\)

On solving the above equation we get,

\({f_2} = 263.5\,{\rm{Hz}}\) or \({f_2} = 264.5\;Hz\) 

Therefore, the possible frequencies are 263.5 Hz and 264.5 Hz.