Question

A tuning fork of frequency $512\, Hz$ makes $4$ beats per second with the vibrating string of a piano. The beat frequency decreases to $2$ beats per sec when the tension in the piano string is slightly increased. The frequency of the piano string before increasing the tension was

• A. 510 Hz
• B. 514 Hz
• C. 516 Hz
• D. 508 Hz

Answer 1

Answer: (D)

Let the frequencies of tuning fork and piano string be $v_{1}$ and
$v_{2}$ respectively
$\therefore v_{2}=v_{1} \pm 4=512 Hz \pm 4 $
$=516 Hz$ or $ 508 Hz$

Increase in the tension of a piano string increases its frequency
If $v_{2}=516 \,Hz$, further increase in $v_{2}$, resulted in an increase in the beat frequency. But this is not given in the question.
If $v_{2}=508 \,Hz$, further increase in $v_{2}$ resulted in decrease in the beat frequency. This is given in the question. When the beat frequency decreases to $2 $ beats per second. Therefore, the frequency of the piano string before increasing the tension was $508\, Hz$.