Question

A pendulum has a frequency of vibrations per second. An observer starts the pendulum and fires a gun simultaneously. He hears the echo from the cliff after 6 vibrations or the pendulum. If the velocity of sound in air is 340 m/s, find the distance between the cliff and the observer.

Answer 1

If the pendulum frequency is \(f\) vibrations per second, then time for 6 vibrations is:

\[d=\frac{v t}{2}\]

\[=\frac{340\times(6/f)}{2}\]

\[=\frac{340\times6}{2\times f}\]

\[=\frac{2040}{2\times f}\]

\[=\frac{1020}{f}\ \text{m}\]

If the intended frequency is 2 vibrations per second, then \(d=510\ \text{m}\). The distance cannot be determined uniquely without the missing frequency.