Respuesta :
Answer:
The average power is 0.1570 W.
Explanation:
Given that,
Mass of piano wire = 3.50 g
Length = 83.0 cm
Tension = 35.0 N
Frequency = 120 Hz
Amplitude = 1.20 mm
Suppose we need to calculate the average power carried by the wave
We need to calculate the angular frequency
Using formula of frequency
[tex]\omega=2\pi f[/tex]
[tex]\omega=2\times\pi\times120[/tex]
[tex]\omega=753.9\ rad/s[/tex]
We need to calculate the linear density
Using formula of linear density
[tex]\mu=\dfrac{M}{l}[/tex]
Put the value into the formula
[tex]\mu=\dfrac{3.50\times10^{-3}}{83\times10^{-2}}[/tex]
[tex]\mu=0.00421\ kg/m[/tex]
[tex]\mu=4.21\times10^{-3}\ kg/m[/tex]
We need to calculate the average power
Using formula of average power
[tex]P_{avg}=\dfrac{1}{2}\sqrt{\mu T}\omega^2\times A^2[/tex]
Put the value into the formula
[tex]P_{avg}=\dfrac{1}{2}\sqrt{4.21\times10^{-3}\times35.0}\times(753.9)^2\times(1.20\times10^{-3})^2[/tex]
[tex]P_{avg}=0.1570\ W[/tex]
Hence, The average power is 0.1570 W.
