Question

A wire of length ${}^{\prime }{L}^{\prime }$ and linear density ${}^{\prime }{m}^{\prime }$ is stretched by a force ${}^{\prime }{T}^{\prime }$ and the frequency is $n_1$. Another wire of the same material of length $2L$ and same density is stretched by a force $9T$ and its frequency is $n_2$. Value of $\left(n_2/n_1\right)$ is:

• A. $1:3$
• B. $3:2$
• C. $1:2$
• D. $4:1$

Answer 1

Answer: (B)

$3:2$

Frequency of wire is given by $n=\frac{\sqrt{\frac{T}{\mu }}}{2l}$

$n\propto \frac{\sqrt{T}}{l}$

Thus, $\frac{n_2}{n_1}=\frac{L}{2L}\sqrt{\frac{9T}{T}}=3:2$