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Question

A transverse wave of amplitude 0.5 mm and frequency 100 Hz is produced on a wire stretched to a tension of 100 N. If the wave speed is 100 m/s. What average power is the source transmitting to the wire?
  1. 60 mJ/s
  2. 49 mJ/s
  3. 40 mJ/s
  4. 70 mJ/s


Solution

The correct option is B 49 mJ/s
Given that,
A=0.5 mm,f=100 Hz,T=100 N,v=100 m/s
Average Power (P)=12ω2A2μv
Wave velocity v=Tμ
μ=Tv2
So, Pav=2π2f2A2(Tv2)v
=2π2f2A2Tv
=2π2(100)2×(0.5×103)2×100100
=0.04934 J/s
P=49.34×10349 mJ/s

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