Question

A light pointer fixed to one prong of a tuning fork touched a vertical plate. The fork is set vibrating and plate is allowed to fall freely. $8$ complete oscillations are counted when the plate falls through $10cm$. What is the frequency of the tuning fork?

• A. $40\sqrt{2}$
• B. $40\sqrt{3}$
• C. $20\sqrt{2}$
• D. $70\sqrt{2}$

Answer 1

The correct option is A $40\sqrt{2}$

The time elapsed when it fell by $d=10cm=0.1m$ can be calculated from:
$d=ut+\frac{1}{2}a{t}^2$
$t=\sqrt{\frac{2d}{g}}=\frac{\sqrt{2}}{10}$
Now, frequency is given by:
$f=\frac{8}{t}=\frac{80}{\sqrt{2}}=40\sqrt{2}$