Answer to Question #207882 in Physics for kamel

Question

A traveling wave on a taut string with a tension force T is given by the wave function: y(x,t) = 0.1sin⁡(2πx-300t), where x and y are in meters and t is in seconds. The linear mass density of the string is μ = 10 g/m, and the string is 10 m-long. The total energy on the string is

Answer 1

The total energy on the string is

$$E=\frac12\mu\omega^2A^2\lambda.$$

As we see from the equation,

$\omega=300\text{ s}^{-1},\\ A=0.1\text{ m},\\ \lambda=\frac{2\pi}{k}=\frac{2\pi}{2\pi}=1\text{ m}.$

Therefore:

$$E=\frac12·0.01·(300)^2(0.1)^2(1)=4.5\text{ J}.$$