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Sagot :
The average power carried by the wave is 0.262. When amplitude is halved, the average power decreases by 4 to 0.065W.
a) The averaged power of a wave on a string is given by Pavg = 1/2 (√(µF)) A^2 w^2
According to the given data,
Mass of piano wire m = 3g = 0.00345kg
Length of piano wire l = 80cm = 0.8m
Tension F = 30 N
Frequency f = 120 Hz
Amplitude A = 1.6mm = 0.0016m
Angular frequency ω = 2πf = 2π (120) = 240π s^-1
Linear mass density μ = m/l = 0.00345/0.8 = 0.00431 kg/m
Hence,
Pavg = 1/2 (√(0.00431*30)) 〖0.0016〗^2 〖(240π)〗^2
Pavg = 0.262W
b) As the average power is always proportional to the square of amplitude, hence
Pavg1/Pavg2 = (A1/A2)^2
0.262/Pavg2 = (0.0016/0.0008)^2
0.262/Pavg2 = 4
Pavg2 = 0.065W
Note: The question is incomplete. The complete question probably is: A piano wire with mass 3.45g and length 80.0 cm is stretched with a tension of 30.0 N. A wave with frequency 120.0 Hz and amplitude 1.6 mm travels along the wire. (a) Calculate the average power carried by the wave. (b) What happens to the average power if the wave amplitude is halved.
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