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

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

Bihar CECEBihar CECE 2001Waves

Solution:

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 $251 Hz$. This is true, because on filing the frequency may increase to 254, giving 2 beats with $B$ of frequency 256 $HZ$