Respuesta :
The average power carried by the wave is 0.29 W
We know that,
[tex]P_{avg}[/tex] = [tex]\frac{1}{2}[/tex] ω² A²√ ( μ F )
ω = 2 π f
μ = m / l
where,
[tex]P_{avg}[/tex] = Average power
ω = Angular speed
A = Amplitude
μ = Linear mass density
F = Tension
f = Frequency
m = Mass
l = Length
Given that,
m = 3.5 g = 0.0035 kg
l = 75 cm = 0.75 m
F = 27 N
f = 120 Hz
A = 1.7 mm = 1.7 * [tex]10^{-3}[/tex] m
μ = m / l = 0.0035 / 0.75
μ = 4.67 * [tex]10^{-3}[/tex] kg / m
ω = 2 π f = 2 * 3.14 * 120
ω = 754 [tex]s^{-1}[/tex]
[tex]P_{avg}[/tex] = [tex]\frac{1}{2}[/tex] ω² A²√ ( μ F )
[tex]P_{avg}[/tex] = [tex]\frac{1}{2}[/tex] ( 754 )² ( 1.7 * [tex]10^{-3}[/tex] )² √ ( 4.67 * [tex]10^{-3}[/tex] * 27 )
[tex]P_{avg}[/tex] = ( 821.5 * [tex]10^{-3}[/tex] ) √ 0.126
[tex]P_{avg}[/tex] = 821.5 * [tex]10^{-3}[/tex] * 0.36
[tex]P_{avg}[/tex] = 0.29 W
Average power is the measure of total work done by the body in a given amount of time.
Therefore, the average power carried by the wave is 0.29 W
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