Question

A piano wire of length 2.5 m vibrates so that one-half wavelength is contained on the string. If the frequency of vibration is 35 Hz, the amplitude of vibration is 3.0 mm, and the density is 20 g/m, how much energy is transmitted per second down the wire?

Answer 1

The energy transmitted per second down the wire is 0.761 watt.

Step-by-step explanation:

Given that,

Length = 2.5 m

Amplitude = 3.0 mm

Density = 20 g/m

Frequency = 35 Hz

We need to calculate the wavelength

Using formula of wavelength

`L = (\lambda)/(2)`

`\lambda=2L`

Put the value into the formula

`\lambda=2*2.5`

`\lambda=5\ m`

We need to calculate the speed

Using formula of speed

`v = f\lambda`

Put the value into the formula

`v =35*5`

`v =175\ m/s`

We need to calculate the energy is transmitted per second down the wire

Using formula of the energy is transmitted per second

`P=(1)/(2)\mu A^2\omega^2* v`

`P=(1)/(2)\mu* A^2*(2\pi f)^2* v`

Put the value into the formula

`P=(1)/(2)*20*10^(-3)*(3.0*10^(-3))^2*4*\pi^2*(35)^2*175`

`P=0.761\ watt`

Hence, The energy transmitted per second down the wire is 0.761 watt.