Question

A small town has decided to forego the use of electrical power and send energy through town via mechanical waves on ropes. They use rope with a mass per length of 1.50 kg/m under 6000 N tension. If they are limited to a wave amplitude of 0.500 m, what must be the frequency of wavesnecessary to transmit power at the average rate of 2.00 kW?

Answer 1

r average --νμωΑ

2*10^3 = 0.5* 1.5* V * [w^2]* .5^2

= velocity = [T/mue]^1/2 = 63.24 m/s

= 2000 = 0.5*1.5* 63.24*w^2*0.25

= w^2 = 168.67

= w =12.98

frequency = w/2*3.24 = 2.06 Hz

Answer 2

P =0.5*W^2*A^2 sqrt(uF)

2000 = W^2*0.5*0.5^2*(1.5*6000)^(1/2)

W = 13

f = W/2pi = 2.07 Hz

Answer 3