Question

A tuning fork $C$ produces $8$ beats per second with another tuning for $D$ of frequency $340Hz$. When the prongs of tuning fork $C$ are filed as little, then number of beats produced per second decreases to $4$. Find the frequency of the tuning fork $C$ before filing its prongs.

Answer 1

Let us consider

Case 1 (Before filing the prongs)

The frequency of tuning fork D=nd=340hz.

Number of beats heard= 8 per second

Therefore, Frequency of tuning fork c before filing the prongs=nc=(340+-8)Hz

Therefore, Frequency of tuning fork c before filing the prongs=332 or 348 Hz

Case 2(When prong c are filed)

Number of beats heard = 4 per second

Therefore, Frequency of tuning fork c after filing the prongs=nc=(340+-4)Hz

Therefore, Frequency of tuning fork c after filing the prongs=336 or 344 Hz

When prongs of the tuning fork are files the frequency of tuning fork increases.

If the frequency of fork c is 348Hz, on filing its frequency should be more than 348 Hz.

It means it cannot take lower values of 344Hz and 336 Hz and hence the frequency of C cannot be 348 Hz.

Hence the frequency of tuning fork c should be 332 Hz, which satisfies the two cases.