Question

Transverse waves are generated in two uniform wires A and B of the same material by attaching their free ends to a vibrating source of frequency $200Hz$. The area of cross section of A is half that of B while tension in A is twice that of B. The ratio of wavelengths of transverse waves in A and B is :

• A. $1:\sqrt{2}$
• B. $\sqrt{2}:1$
• C. $1:2$
• D. $2:1$

Answer 1

The correct option is D $2:1$

Velocity $v=\sqrt{\frac{T}{\mu }}$ = $\sqrt{\frac{T}{\rho A}}$

$\lambda =\frac{v}{\nu }$

As frequency of wave and density of material is same for A and B

$\frac{{\lambda }_A}{{\lambda }_B}=\sqrt{\frac{T_A{A}_B}{T_B{A}_A}}=2:1$