1. Tardigrade
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  4. A tuning fork A produces 4 beats with tuning fork B of frequency 256 Hz. When A is filed beats are found to occur at shorter intervals. What was its original frequency of tuning fork A ?

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Q. A tuning fork $A$ produces $4$ beats with tuning fork $B$ of frequency $256\, Hz$. When $A$ is filed beats are found to occur at shorter intervals. What was its original frequency of tuning fork $A$ ?

Waves

Solution:

As tuning fork $A$ produces $4$ beats with tuning fork $B$ of frequency $v_{B}(=256\, Hz )$, the frequency of $A\left(v_{A}\right)$ will be
$v_{A}=v_{B} \pm 4=256 \pm 4, \text { i.e., } v_{A}=252 Hz $ or $ 260\, Hz$
Now on filing due to decrease in inertia frequency of $A$ will increase and occurrence of beats at shorter duration means increase in beat frequency; so if
$v_{A}=252 Hz$, then
$256- v _{A}=4 Hz$
and so with increase in $v_{A}$ beat frequency will decrease.
If $v_{A}=260\, Hz$, then
$v_{A}-256=4 \,Hz$
and so with increase in $v_{A}$ beat frequency will increase and as on filing beat frequency increases the frequency of $A$ before filing was $260 \,Hz$.