Solve this following

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 ?

  1. $342 \mathrm{~Hz}$

  2. $345 \mathrm{~Hz}$

  3. $335 \mathrm{~Hz}$

  4. $338 \mathrm{~Hz}$

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 $\rho_{\mathrm{A}}=335 \mathrm{~Hz}$

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