Question

A tuning fork of frequency 280 Hz produces 10 beats per sec when sounded with a vibrating sonometer string. When the tension in the string increases slightly, it produces 11 beats per sec. The original frequency of the vibrating sonometer string is :

• A. 269 Hz
• B. 291 Hz
• C. 270 Hz
• D. 290 Hz

Answer 1

The correct option is C 270 Hz

Let,
The frequency of tuning fork is ${\nu }_T=280Hz$

The frequency of the sonometer string is ${\nu }_s$

The frequency of beats is

$|{\nu }_T-{\nu }_s|=10$

Hence, the frequency of sonometer string is either $10Hz$ more i.e. $290Hz$ or $10Hz$ less i.e. $270Hz$ because the increase in this frequency will reduce the frequency of beats.

But when tension is applied to the string its frequency increases and the number of beats also increases. Hence, the frequency of string cannot be $290Hz$.
Therefore the frequency of the sonometer string is $270Hz$.