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