Question

A taut rope has a mass of 0.129 kg and a length of 3.70 m. What average power must be supplied to the rope to generate sinusoidal waves that have amplitude 0.200 m and wavelength 0.600 m if the waves are to travel at 24.0 m/s?

Answer 1

Power generated will be equal to 1054.046 watt

Step-by-step explanation:

We have given mass m = 0.129 kg

Length of the rope = 3.70 m

So mass density
`\mu =(m)/(l)=(0.129)/(3.7)=0.0348kg/m`

Amplitude A = 0.200 m

Wavelength = 0.600 m

Velocity of the wave v = 24 m/sec

So frequency
`f=(v)/(\lambda )=(24)/(0.600)=40Hz`

Now angular frequency will be equal to
`\omega =2\pi f=2* 3.14* 40=251.2rad/sec`

We have to fond the generated power

Power will be equal to
`P=(1)/(2)\mu \omega ^2A^2v=(1)/(2)* 0.0348* 251.2^2* 0.2^2* 24=1054.046watt`

So power generated will be equal to 1054.046 watt