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Question

A tuning fork A of unknown frequency produces 4 beats per second when sounded with another tuning fork B of frequency 254 Hz. When tuning fork A is loaded with wax, it still gives 4 beats per second with tuning fork A. The initial unknown frequency of tuning fork A is

A
258 Hz
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B
254 Hz
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C
250 Hz
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D
262 Hz
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Solution

The correct option is A 258 Hz
Given,
fb=4 Hz
We know, beat frequency
fb=|f1f2|
f2=f1±fb
Frequency of tuning fork B,
f1=254 Hz
f2=254±4 Hz
So, frequency of tuning fork A can be,
f2=250 Hz or 258 Hz
As the tuning fork A is loaded with wax, therefore its time period should increase and frequency should decrease.
So, by intuition, the initial frequency should be 258 Hz which will decrease to 250 Hz when loaded with wax.

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