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Byju's Answer

Standard XII

Physics

Wavelength

Transverse wa...

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 $200 H z$ . The area of cross section of A is half that of B while tension in A is twice that of B. The ratio of wavelengths of transverse waves in A and B is :

1 : \sqrt{2}

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\sqrt{2} : 1

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1 : 2

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2 : 1

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Solution

The correct option is D $2 : 1$
Velocity $v = \sqrt{\frac{T}{μ}}$ = $\sqrt{\frac{T}{ρ A}}$
$λ = \frac{v}{ν}$

As frequency of wave and density of material is same for A and B
$\frac{λ_{A}}{λ_{B}} = \sqrt{\frac{T_{A} A_{B}}{T_{B} A_{A}}} = 2 : 1$

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The correct option is D 2:1Velocity v=√Tμ = √TρAλ=vνAs frequency of wave and density of material is same for A and B λAλB=√TAABTBAA=2:1

The correct option is D $2 : 1$
Velocity $v = \sqrt{\frac{T}{μ}}$ = $\sqrt{\frac{T}{ρ A}}$
$λ = \frac{v}{ν}$

As frequency of wave and density of material is same for A and B
$\frac{λ_{A}}{λ_{B}} = \sqrt{\frac{T_{A} A_{B}}{T_{B} A_{A}}} = 2 : 1$