Question:
A tuning fork A of unknown frequency produces 5 beats/s with a fork of known frequency $340 \mathrm{~Hz}$. When fork $\mathrm{A}$ is filed, the beat frequency decreases to 2 beats/s. What is the frequency of fork A ?
Correct Option: , 3
Solution:
Initially beat frequency $=5 \mathrm{~Hz}$
so, $\rho_{\mathrm{A}}=340 \pm 5=345 \mathrm{~Hz}$, or $335 \mathrm{~Hz}$
after filing frequency increases slightly
so, new value of frequency of $\mathrm{A}>\rho_{\mathrm{A}}$
Now, beat frequency $=2 \mathrm{~Hz}$
$\Rightarrow$ new $\rho_{\mathrm{A}}=340 \pm 2=342 \mathrm{~Hz}$, or $338 \mathrm{~Hz}$
hence, original frequency of $\mathrm{A}$ is $\rho_{\mathrm{A}}=335 \mathrm{~Hz}$