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 $200\text{Hz}$. The cross-sectional area of $A$ is half that of $B$ while the tension on $A$ is twice that on $B$. The ratio of the wavelengths of the 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 $2:1$

$v=\nu \lambda$ or $v\propto \lambda [\because \nu \text{is constant}]$
$\lambda \propto v$
$\lambda \propto \sqrt{\frac{T}{m}}$
$\lambda \propto \sqrt{\frac{T}{Ad}}$
$\lambda \propto \sqrt{\frac{T}{A}}$
$\frac{{\lambda }_A}{{\lambda }_B}=\sqrt{\frac{2T\times 2}{A}\times \frac{A}{T}}=\frac{2}{1}$