Question

A tuning fork produces S beats/s with another tuning fork B of frequency $256Hz$. On filing fork A only $2$ beats are heard per second, the frequency of A before filing is:

• A. 251 Hz
• B. 254 Hz
• C. 261 Hz
• D. 256 Hz

Answer 1

Answer: (A)

There are 5 beats between $A$ and $B$, therefore the possible frequencies of $A$ are 251 or 261 (that is $256\pm 5$ ) $Hz$. When the prong of $A$ is filed, its frequency becomes greater than the original frequency. If we assume that the original frequency of $A$ is 261, then on filling its frequency will be greater than 261 . The beats between $A$ and $B$ will be more than $5.$ But it is given that the beats are reduced to 2 , therefore 261 is not possible. Therefore, the required frequency must be $251Hz$. This is true, because on filing the frequency may increase to 254, giving 2 beats with $B$ of frequency 256 $HZ$