Question

A tuning fork produces $8$ beats per second when sounded together with a fork of frequency $340Hz.$ When the prongs of tuning fork C are filled a little, the number of beats produced per second decreases to 4. Find the frequency of the tuning fork C before filling its prongs$.$

• A. $332Hz$
• B. $434Hz$
• C. $430Hz$
• D. $436Hz$

Answer 1

The correct option is A $332Hz$

given :

$n_D=$ tuning fork $D$ frequency $=340Hz$

$n_C=$ tuning fork $C$ frequency$=8–4=4$ beats per second$.$

First $n_C\pm n_D=8($before filing$)$

$n_C\pm n_D=4($after filing$)$

From given condition $n_c\pm nD=8$

$\therefore n_c\pm 340=8$

$\therefore n_c=340+8=348Hz$

or$,n_c=340–8=332Hz$

when tuning fork C is filed then $n_c\pm nD=4$

$\therefore n_c\pm 340=4$

$\therefore n_c=340+4=344Hz$

or$,n_c=340–4=336Hz$

The frequency of tuning fork increases on filing. Hence $n_c\ne 344Hz.$

If original frequency of tuning fork C is taken 332 Hz, then on filing both the value $344Hz,$ and $336Hz$ are greater$.$

Also it produces $4$ beats per second with tuning fork $D.$

$\therefore$ frequency of tuning fork $C=332Hz$

Hence,

option $\left(A\right)$ is correct answer.