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Q.

Transverse wave are generated in two uniform steel wires A & B of same length but having diameters  10−3m and 0.5×10−3m 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

12

b

4

c

5

d

6

answer is A.

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Detailed Solution

Wave Speed  v=Tμ ∴vAvB=μBμA=dBdA   {μ=Ml=πd2ρ4} Also v=nλ ⇒v∝λ  Hence, we can say ∴vAvB=λAλB=dBdA=0.5×10−310−3=0.5=12
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