Question

Two vibrating strings are of same material but lengths l, 2l and radii 2r, r respectively are stretched under the same tension. Both are vibrating in their fundamental modes. The experimental arrangement is such that first string has both ends fixed, second string vibrates with one end fixed and other end as free.

If the frequencies of vibration of first and second wire are $n_1$ and $n_2$, then $\frac{n_1}{n_2}$= ________

• A. 2
• B. 6
• C. 3
• D. 4

Answer 1

The correct option is A

2

Both ends fixed :- $n_1$ = $\frac{1}{2l_1}$ $\sqrt{\frac{T}{{\mu }_1}}$ = $\frac{1}{2l_1}$$\sqrt{\frac{T}{\pi {r_1}^2\rho }}$

One end fixed :- $n_2$ = $\frac{1}{4l_2}$ $\sqrt{\frac{T}{{\mu }_2}}$ = $\frac{1}{4l_2}$ $\sqrt{\frac{T}{\pi {r_2}^2\rho }}$

$\frac{n_1}{n_2}$ = $\frac{4l_2}{2l_1}$ $\frac{r_2}{r_1}$ = 2