First slide

Standing waves

Question

Transverse waves are generated in two uniform wires A and B of same material by attaching their free ends to a vibrating source of frequency 200 Hz. The cross-sectional area 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

Easy

A

1: $\sqrt{2}$
B

$\sqrt{2 : 1}$
C

1:2
D

2:1

Solution

$as n is constant \frac{v_{1}}{λ_{1}} = \frac{v_{2}}{λ_{2}} n = \frac{p}{2 l} \sqrt{(\frac{T}{{πr}^{2} ρ})} = \frac{p}{2 l} \sqrt{(\frac{T}{Aρ})} ∴ \frac{v_{1}}{v_{2}} = \frac{λ_{1}}{λ_{2}} = {[\frac{T_{1}}{T_{2}} \times \frac{A_{2}}{A_{1}}]}^{1 / 2} = {[\frac{2 T}{T} \times \frac{A}{(A / 2)}]}^{1 / 2} = \frac{2}{1}$

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