Question

Two stretched strings have lengths $l$ and $2l$ while tensions are $T$ and $4T$ respectively: If they are made of same material the ratio of their frequencies is

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

Answer 1

The correct option is C $1:1$

Frequency, $\nu =\frac{1}{2l}\sqrt{\frac{T}{\mu }}$ where $\mu$ is mass per unit length

$⟹$ $\nu \propto \frac{\sqrt{T}}{L}$

Thus, $\frac{{\nu }_1}{{\nu }_2}=\frac{\sqrt{T_1}}{L_1}.\frac{L_2}{\sqrt{T_2}}$

We get $\frac{{\nu }_1}{{\nu }_2}=\frac{\sqrt{T}}{l}.\frac{2l}{\sqrt{4T}}=1$

$⟹$ ${\nu }_1:{\nu }_2=1:1$