When a guitar string is sounded with a $440 \mathrm{~Hz}$ tuning fork, a beat frequency of $5 \mathrm{~Hz}$ is heard. If the experiment is repeated with a tuning fork of $437 \mathrm{~Hz}$, the beat frequency is $8 \mathrm{~Hz}$. The string frequency (Hz) is

• Correct answer
  A

  445
• B

  435
• C

  429
• D

  448 .

Solution

$v-5=440 \mathrm{~Hz}$ $$ \begin{aligned} & v-8=437 \mathrm{~Hz} \\ & \therefore v=445 \mathrm{~Hz} \text { by both the } \\ & \text { methods. } \end{aligned} $$
It could have been $435 \mathrm{~Hz}$. It would have satisfied $440-v=5$. But this would not have satisfied $437 \mathrm{~Hz}$.

Hence, the correct answer is option: 'A'.