Q59PE - College Physics (Urone)

Question

Two tuning forks having frequencies of 460 and 464 Hz are struck simultaneously. What average frequency will you hear, and what will the beat frequency be?

Step-by-Step Solution

Answer

The average frequency of two forks is 462 Hz and beat frequency is 4 Hz.

Step 1: Introduction

We calculate beat frequency of two horns as we know that beat frequency is modulus of difference of two frequencies. We also calculate average frequency of two forks.

Step 2: Given parameters and formula for beat frequency and average frequency

Frequency of first fork         \( = 460 Hz\)

Frequency of second fork    \( = 464 Hz\)

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

Average frequency \({f_{avg}}   = ({f_1} + {f_2})/2\)

Here, 

\({f_1},{f_2}\) - frequency of 2 sources.

\(f\)   - beat frequency.

\({f_{avg}} \)-average frequency.

Step 3: Calculate beat frequency and average frequency

Beat frequency of two forks is

\(\begin{align}{\underline{\phantom{xx}}}f &= \left| {{f_1} - {f_2}} \right|\\f &= \left| {460 - 464} \right|Hz\\f &= 4Hz\end{align}\)

Average frequency of two forks is

\(\begin{align}{\underline{\phantom{xx}}}{f_{avg}} &= ({f_1} + {f_2})/2\\{f_{avg}} &= (460 + 464)/2\\{f_{avg}} &= 462 Hz\end{align}\)

 

Therefore, the average frequency of two forks is 462 Hz and beat frequency is 4 Hz.