Question

A tuning fork of frequency 480 Hz produces 10 beats/s when sounded with a vibrating sonometer string. What must have been the frequency of the string if a slight increase in tension produces fewer beats per second than before?

• A. 460 Hz
• B. 480 Hz
• C. 490 Hz
• D. 470 Hz

Answer 1

The correct option is D 470 Hz

As tension increases, frequency increases in the string as $f\propto \sqrt{T}$
where $T$ is tension,

increase in tension in the string frequency of the string increases and as given in problem ,

beats decreases so frequency of string must be less than frequency of fork.

So, Beat =frequency of fork $-$ frequency of string

$10=480Hz-f_s$

$\Rightarrow$frequency of string$=470H_z$