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

Answer:

Power generated will be equal to 1054.046 watt  

Explanation:

We have given mass m = 0.129 kg

Length of the rope = 3.70 m

So mass density $\mu =\frac{m}{l}=\frac{0.129}{3.7}=0.0348kg/m$

Amplitude A = 0.200 m

Wavelength = 0.600 m

Velocity of the wave v = 24 m/sec

So frequency $f=\frac{v}{\lambda }=\frac{24}{0.600}=40Hz$

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

We have to fond the generated power

Power will be equal to $P=\frac{1}{2}\mu \omega ^2A^2v=\frac{1}{2}\times 0.0348\times 251.2^2\times 0.2^2\times 24=1054.046watt$

So power generated will be equal to 1054.046 watt