Question

A sonometer wire vibrates with frequency $n_1$ in air under suitable load of specific gravity $\sigma$. When the load is immersed in water, the frequency of vibration of wire $n_2$ will be

• A. $n_1\sqrt{\frac{\sigma +1}{\sigma }}$
• B. $n_1\sqrt{\frac{\sigma -1}{\sigma }}$
• C. $n_1\sqrt{\frac{\sigma }{\sigma +1}}$
• D. $n_1\sqrt{\frac{\sigma }{\sigma -1}}$

Answer 1

Answer: (B)

$n_1\sqrt{\frac{\sigma -1}{\sigma }}$

Specific gravity or relative density is

$\frac{n_1}{n_2}=\sqrt{\frac{\sigma }{\sigma -1}}$

$\therefore n_2=n_1\sqrt{\frac{\sigma -1}{\sigma }}$