Chapter 15, Problem 15.48P

A transverse wave on a rope is given by

$y\left(x,t\right)=\left(0.750\text{ cm}\right)\cos \pi \left[\left(0.400{\text{ cm}}^{\text{-1}}\right)x+\left(250{\text{ s}}^{\text{-1}}\right)t\right]$

(a) Find the amplitude, period, frequency, wavelength, and speed of propagation. (b) Sketch the shape of the rope at these values of t: 0, 0.0005 s, 0.0010 s. (c) Is the wave traveling in the +x- or −x-direction? (d) The mass per unit length of the rope is 0.0500 kg/m. Find the tension. (c) Find the average power of this wave.