First slide

Speed of wave

Question

Transverse waves are generated in two uniform steel
wires A and B by attachilg their free end to vibrating
source of frequency 500 Hz. The diameter of wire A is
half that of wire B and the tension on wire A is half that
on wire B. What is ratio of the velocity of waves in
wires A and B?

Moderate

A

1:2
B

2:1
C

1 : $\sqrt{2}$
D

$\sqrt{2} : 1$

Solution

$V = \sqrt{(\frac{T}{m})} = \sqrt{(\frac{T}{{πr}^{2} ρ})} V \propto \frac{\sqrt{T}}{D} where D = diameter \frac{v_{1}}{v_{2}} = {(\frac{T_{1}}{T_{2}})}^{1 / 2} \times \frac{D_{2}}{D_{1}} = {[\frac{T / 2}{T}]}^{1 / 2} [\frac{D}{(D / 2)}] = \frac{2}{\sqrt{2}} = \frac{\sqrt{2}}{1}$

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