Question

A sonometer wire of length $L$ is plucked at a distance $L/8$ from one end then it vibrates with a minimum frequency $n$ . If the same wire is plucked at a distance $L/6$ from another end, the minimum frequency with which it vibrates is

• A. $\frac{\sqrt{3}}{2}n$
• B. $\frac{3}{2}n$
• C. $\frac{3n}{4}$
• D. $\frac{4n}{3}$

Answer 1

The correct option is C $\frac{3n}{4}$

The length at which the minimum frequency of sonometer wire vibrates is $l=\lambda /4$. Here, according to the question:
$l=L/8=\lambda /4$ or $\lambda =L/2$, so the frequency will be $n=V/\lambda =2V/L$.
From the other end:
$l=L/6=\lambda /4$ or $\lambda =2L/3$, so the frequency will be $n_1=V/\lambda =3V/2L=3n/4$.