A transverse wave of amplitude 0.5mm and frequency 100Hz is produced on a wire stretched to a tension of 100N. If the wave speed is 100m/s. What average power is the source transmitting to the wire?
A
60mJ/s
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B
49mJ/s
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C
40mJ/s
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D
70mJ/s
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Solution
The correct option is B49mJ/s Given that, A=0.5mm,f=100Hz,T=100N,v=100m/s Average Power (P)=12ω2A2μv Wave velocity v=√Tμ ⇒μ=Tv2 So, Pav=2π2f2A2(Tv2)v =2π2f2A2Tv =2π2(100)2×(0.5×10−3)2×100100 =0.04934J/s ⇒P=49.34×10−3≈49mJ/s