Question

Tuning fork $A$ of frequency $305Hz$ produces $5beats/s$ with another tuning fork $B$. After filing tuning fork $B$, it produces $3beats/s$ with $A$. The frequency of $B$ before filing was:

• A. $300Hz$
• B. $313Hz$
• C. $310Hz$
• D. $308Hz$

Answer 1

The correct option is A $300Hz$

The phenomenon of beats is used in the determination of unknown frequencies.
Suppose $v_2$ is the unknown frequency of a tuning fork $B$. Let this fork $B$ produce $m$ beats per second with another tuning fork $A$ of known frequency $v_1$.
As number of $beats/s$ is equal to difference in frequency of two sources.
Therefore, $v_2=v_1\pm m$
When the prong of fork $B$ is filled a little, it becomes lighter and its frequency of vibration increases on sounding the filed fork $B$ with fork $A$, we count the number of $beats/s$.
Proceeding as, we conclude that, if number of $beats/s$ on filing fork $B$ of unknown frequency increases, $m$ would be positive and vice-versa. So, frequency of tuning fork $B=305\pm 5=310Hz,300Hz$
Since, on filling tuning fork $B$, number of beats decreases. This means that frequency of $B$ should be less ie., $300Hz$.