Question

A tuning fork of unknown frequency gives 4 beats with a tuning fork of frequency 310 Hz. It gives the same number of beats on filing. Find the unknown frequency.

Answer 1

The unknown frequency of the tuning fork can be 

= 310 ± 4 

or f = 314 or 306 Hz 

Suppose f = 314 Hz 

On filing, let it becomes = 318 Hz. 

When it sounded together with a fork of frequency 310 Hz, beats frequency will be more than 4 per second. Therefore unknown frequency can not be 314 Hz. 

Now suppose f = 306 Hz. 

On filing, let it becomes = 314 Hz. 

When it sounded again with a fork of frequency 310 Hz it gives 4 beats per second. So unknown frequency must be 306 Hz.