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A tuning fork A produces 8 beats per second with a fork B of frequency 320 Hz. When the prongs of A are filed a little, the beats occur at shorter intervals. The frequency of A before filing is 

A tuning fork A produces 8 beats per second with a fork B of frequency 320 Hz. When the prongs of A are filed a little, the beats occur at shorter intervals. The frequency of A before filing is  Correct Answer 328 Hz

Concept:

Beats: When two waves of nearly equal frequencies travelling in a medium along the same direction superimpose upon each other, beats are produced. The amplitude of the resultant sound at a point rises and falls regularly.

The count of beats per second is equivalent to the difference in frequencies of two waves is called beat frequency. It is because of constructive and destructive interference. 

fb = |f1 – f2|

Calculation:

Given fb = 320 Hz, fb = 8 beats per second = 8 Hz;

From the beat frequency formula,

8 = |fa - 320| ⇒ fa = 328 or 312 Hz

When prongs are filed a little, the frequency of tuning fork increases.

Now beats are heard at shorter intervals that is number of beats per second increases.

If fa = 312 Hz, increase in frequency (say 316 Hz) decreases number of beats per second (4), which is not the case.

If fa = 328 Hz, increase in frequency (say 332 Hz) increases number of beats per second (12), which is the given case.

Hence, the frequency of tuning fork A is 328 Hz

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