Question

A string oscillating at a fundamental frequency under a tension of 225 N produces 6 beats/sec with a sonometer. If the tension is 256 N, then again oscillating at fundamental note it produces 6 beats per second with the same sonometer. The frequency of the sonometer is:

• A. 256 Hz
• B. 225 Hz
• C. 280 Hz
• D. 186 Hz

Answer 1

The correct option is D 186 Hz

Fundamental frequency of the string $f=1/2l\left(\sqrt{T/\mu }\right)$

so in case of 225 newton tension $f_1=15/2l\left(\sqrt{1/\mu }\right)$

and in case of 256 N tension $f_2=16/2l\left(\sqrt{1/\mu }\right)$

on increasing tension the frequency also increases ,and as given on increasing frequency the no of beats are same, so the initial frequency of string was 6 less than sonometer and final frequency of string is 6 more than sonometer as both time 6 beats were produced.

$f_2-f_1$ =$12$ (as described above)

$12=1/2l\left(\sqrt{1/\mu }\right)$ (difference between $f_{2}and{f}_1$ calculated from above equations )

as,

$f_1=15/2l\left(\sqrt{1/\mu }\right)$

$f_1=180$

frequecy of sonometer will be 6 more than $f_1$

$f_{sonometer}=186$

Correct answer is $D$.