Question

A piano wire with mass 3.50 g and length 83.0 cm is stretched with a tension of 35.0 N. A wave with frequency 120 Hz and amplitude 1.20 mm travels along the wire.

Answer 1

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

$\omega=2\pi f$

$\omega=2\times\pi\times120$

$\omega=753.9\ rad/s$

We need to calculate the linear density

Using formula of linear density

$\mu=\dfrac{M}{l}$

Put the value into the formula

$\mu=\dfrac{3.50\times10^{-3}}{83\times10^{-2}}$

$\mu=0.00421\ kg/m$

$\mu=4.21\times10^{-3}\ kg/m$

We need to calculate the average power

Using formula of average power

$P_{avg}=\dfrac{1}{2}\sqrt{\mu T}\omega^2\times A^2$

Put the value into the formula

$P_{avg}=\dfrac{1}{2}\sqrt{4.21\times10^{-3}\times35.0}\times(753.9)^2\times(1.20\times10^{-3})^2$

$P_{avg}=0.1570\ W$

Hence, The average power is 0.1570 W.