Question

A wire with linear density of 3 gm/mm is used as a sonometer wire for producing vibrations of frequency 50 Hz. This length of this wire is now halved, while the tension is reduced by 1/4th of the initial tension. What will be the frequency of vibrations produced:

• A. 10 Hz
• B. 30 Hz
• C. 50 Hz
• D. 70 Hz

Answer 1

The correct option is C 50 Hz

The frequency of vibration in a sonometer is given by $f=\left(1/2L\right)\sqrt{(}T/\mu )$
since length is halved and tension is made 1/4th the initial tension, their ratio $\sqrt{(}T)/L$ remains constant. Thus, frequency now depends only on linear mass density
Since the same wire is used, linear mass density dosen't change and hence the frequency also remains same
The correct option is (c)