A tuning fork A of unknown frequency produces 5 beats/s with a fork of frequency 340Hz. When fork A is filed, the beat frequency decreases to 2 beats/s/ What is the initial frequency of fork A before filing ?

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A tuning fork A of unknown frequency produces $5 beats / s$ with a fork of frequency 340Hz. When fork A is filed, the beat frequency decreases to $2 beats / s$ / What is the initial frequency of fork A before filing ?

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335 Hz

345 Hz

342 Hz

338 Hz

answer is C.

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Detailed Solution

Initially beat frequency = 5 Hz
so, $ρ_{A} = 340 \pm 5 = 345 Hz$ , or 335 Hz
After filing frequency increases slightly
so, new value of frequency of $A > ρ_{A}$
Now, beat frequency = 2 Hz
⇒ new $ρ_{A} = 340 \pm 2 = 342 Hz$ , or 335Hz
hence, original frequency of A is $ρ_{A} = 335 Hz$