Question

The system of two rods shown in figure is vibrating at the same frequency and forming a standing wave. The ratio of the number of antinodes in the two rods if radius of rod B is twice the radius of A is :

• A. $1$
• B. $2$
• C. $3$
• D. $4$

Answer 1

Answer: (B)

$2$

$f_1=\frac{n}{2\ell }\sqrt{\frac{T}{\rho A}}$ $f_2=\frac{m}{2\ell }\sqrt{\frac{T}{\rho 4A}}$
Given $f_1=f_2$
$\frac{f_1}{f_2}=\frac{n}{m}\times 2$
$\frac{n}{m}=2$