Question

Transverse waves of the same frequency are generated in two steel wires $A$ and $B$. The diameter of $A$ is twice of $B$ and the tension in $A$ is half that in $B$. The ratio of the velocities of waves in $A$ and $B$ is

• A. $1:2\sqrt{2}$
• B. $3:2\sqrt{2}$
• C. 1:2
• D. $1:\sqrt{2}$

Answer 1

Answer: (A)

${\upsilon }_{wave}=\sqrt{\frac{T}{m}}=\sqrt{\frac{T}{\rho \frac{\pi d^2}{4}l}}$ i.e. ${\upsilon }_{wave}\propto \sqrt{\frac{T}{d}}$
$\therefore$ $\frac{{\upsilon }_{waveA}}{{\upsilon }_{waveB}}=\sqrt{\frac{T_A}{T_B}}\times \frac{d_B}{d_A}=\sqrt{\frac{\frac{1}{2}{T}_B}{T_B}}\times \frac{d_B}{2d_A}=\frac{1}{2\sqrt{2}}$