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

The average power is 0.1570 W.

Step-by-step 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*\pi*120`

`\omega=753.9\ rad/s`

We need to calculate the linear density

Using formula of linear density

`\mu=(M)/(l)`

Put the value into the formula

`\mu=(3.50*10^(-3))/(83*10^(-2))`

`\mu=0.00421\ kg/m`

`\mu=4.21*10^(-3)\ kg/m`

We need to calculate the average power

Using formula of average power

`P_(avg)=(1)/(2)√(\mu T)\omega^2* A^2`

Put the value into the formula

`P_(avg)=(1)/(2)\sqrt{4.21*10^(-3)*35.0}*(753.9)^2*(1.20*10^(-3))^2`

`P_(avg)=0.1570\ W`

Hence, The average power is 0.1570 W.