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Q.

Transverse wave are generated in two uniform steel wires A & B of same length but having diameters $10^{- 3} m$ and $0.5 \times 10^{- 3} m$ respectively, by attaching their free end to a vibrating source of frequency 500 Hz. Find the ratio of the wavelengths if they are stretched with the same tension.

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a

$\frac{1}{2}$

b

4

c

5

d

6

answer is A.

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Detailed Solution

$W a v e S p e e d v = \sqrt{\frac{T}{μ}} ∴ \frac{v_{A}}{v_{B}} = \sqrt{\frac{μ_{B}}{μ_{A}}} = \frac{d_{B}}{d_{A}} {μ = \frac{M}{l} = \frac{π d^{2} ρ}{4}} A l s o v = n λ \Rightarrow v \propto λ H e n c e, w e c a n s a y ∴ \frac{v_{A}}{v_{B}} = \frac{λ_{A}}{λ_{B}} = \frac{d_{B}}{d_{A}} = \frac{0.5 \times 10^{- 3}}{10^{- 3}} = 0.5 = \frac{1}{2}$

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