A 200 Hz wave with amplitude 1 mm travels on a long string of linear mass density 6 g m−1 kept under a tension of 60 N. (a) Find the average power transmitted across a given point on the string. (b) Find the total energy associated with the wave in a 2.0 m long portion of the string.
A=1mm=10−3m,
m=6g/m=6×10−3kg/m
T = 60 N, f = 200 Hz
V=√(Tm)=√(60)(6×10−3)=102=100 m/s
(a) Paverage=2π2mv A2f2
=2×(3.14)2×(6×10−3)×100×(10−3×2002)
=473×10−3=0.47 W
(b) Length of the string is 2m.
So, t=2100=0.02 sec
Energy =2π2mvf2A2t
=2×(3.14)2×6×(10−3)×100×2002×(10−3)2×(0.02)
=946.5×10−5
=9.46×10−3J=9.46 mJ