Question

A source of unknown frequency gives $4\text{beats/s,}$ when sounded with a source of frequency $250\text{Hz}.$ The second harmonic of the source of an unknown frequency gives $5\text{beats/s,}$ when sounded with a source of frequency $513\text{Hz}.$ The unknown frequency is-

• A. $260\text{Hz}$
• B. $254\text{Hz}$
• C. $246\text{Hz}$
• D. $240\text{Hz}$

Answer 1

The correct option is B $254\text{Hz}$

Frequency of the unknown source can be,

$f^{\prime }=f\pm 4=246\text{Hz}\text{or}254\text{Hz}$


Second harmonic of the source is

$2f^{\prime }=492\text{Hz}\text{or}508\text{Hz}$

When the second harmonic is sounded with a source of frequency $513\text{Hz}$, it gives $5$ beats per sound.

Hence, $2f^{\prime }=508+5=513\text{Hz},$ is the only possible value.

Therefore, the unknown frequency is $f^{\prime }=254\text{Hz}$

<!--td {border: 1px solid #ccc;}br {mso-data-placement:same-cell;}--> Hence, $\left(B\right)$ is the correct answer.