Question

The fundamental frequency of a sonometer wire increases by 6 Hz, if its tension is increased by 44%, keeping the length constant. Find the change in the fundamental frequency of the sonometer wire when the length of the wire is increased by 40%, keeping the original tension in the wire constant.

• A. 8.6 Hz
• B. 21.4 Hz
• C. 51.4 Hz
• D. 17.2 Hz

Answer 1

The correct option is A 8.6 Hz

Fundamental frequency, $f_0=\frac{1}{2l}\sqrt{\frac{T}{\mu }}$
When frequency is increased by 44%, frequency, $f=\frac{1}{2l}\sqrt{\frac{1.44T}{\mu }}=1.2f_0$
Now, $1.2f_0-f_0=6\Rightarrow f_0=30Hz$
When length is increased by 40%, $f^{\prime }=\frac{1}{2\times 1.4l}\sqrt{\frac{T}{\mu }}=\frac{f_0}{1.4}=21.4Hz$
Change in frequency $=30-21.4=8.6Hz$