Question

A sinusoidal wave of angular frequency 1,203 rad/s and amplitude 3.1 mm is sent along a cord with linear density 3.9 g/m and tension 1,871 N. What is the average rate at which energy is transported by the wave to the opposite end of the cord? Give SI unit.

Answer 1

18.7842493212 W

Step-by-step explanation:

T = Tension = 1871 N

`\mu` = Linear density = 3.9 g/m

y = Amplitude = 3.1 mm

`\omega` = Angular frequency = 1203 rad/s

Average rate of energy transfer is given by

`P=(1)/(2)√(T\mu)\omega^2y^2\\\Rightarrow P=(1)/(2)\sqrt{1871* 3.9* 10^(-3)}* 1203^2* (3.1* 10^(-3))^2\\\Rightarrow P=18.7842493212\ W`

The average rate at which energy is transported by the wave to the opposite end of the cord is 18.7842493212 W