First slide

Stationary waves

Question

Transverse waves of 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 velocities of wave in A and B is

Moderate

A

$1 : 3 \sqrt{2}$
B

$1 : 2 \sqrt{2}$
C

$1 : 2$
D

$\sqrt{2} : 1$

Solution

$v = \sqrt{\frac{T}{m}} = \sqrt{\frac{T}{{πr}^{2} ρ}}$
$v \propto \frac{\sqrt{T}}{r} \Rightarrow \frac{v_{A}}{v_{B}} = \sqrt{\frac{T_{A}}{T_{B}}} . \frac{r_{B}}{r_{A}} = \sqrt{\frac{1}{2}} . \frac{1}{2} = \frac{1}{2 \sqrt{2}}$

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