A transverse wave having amplitude A=4πm and frequency f=2Hz is travelling on a string of linear mass-density μ=1kg/m. If the total kinetic energy associated with one wavelength of the wave is 16J. Then the wavelength of the transverse wave is
A
0.5m
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B
0.25m
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C
0.75m
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D
0.15m
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Solution
The correct option is B0.25m Total kinetic energy associated with one wavelength of the wave is given by, Kλ=14μA2ω2λ ∵ω=2πf=2π×2=4πrad/s and A=4πm,μ=1kg/m ⇒Kλ=14×λ×1×(4π)2×(4π)2 ⇒16=14×λ×16×16 ⇒λ=14m=0.25m