Question

A light pointer fixed to one prong of a tuning fork touches a vertical plate. The fork is set vibrating and the plate is allowed to fall freely. Eight complete oscillations are counted when the plate falls through $10 \,cm$. What is the frequency of the fork?

Answer 1

During the time the plate falls through $10\, cm$ from rest, the tuning fork makes $8$ vibrations.
From speed equation we get, $h=\frac{1}{2} g t^{2}$
$0.1=\frac{1}{2} \times 9.8 \times t^{2}$ or $t=\frac{1}{7} s$
In $\frac{1}{7} s$ the fork makes $8$ vibrations. Therefore, in Is, the number of vibrations fork makes, $n=8 \times 7=56$
Thus, frequency of fork is, $n=56\, Hz$