Chapter 16, Problem 57P

A generator at one end of a very long string creates a wave given by

$y=\left(6.0\text{cm}\right)\cos \frac{\pi }{2}\left[\left(2.00{\text{m}}^{-1}\right)x+\left(8.00{\text{s}}^{-1}\right)t\right],$

and a generator at the other end creates the wave

$y\text{= }\left(6.0\text{cm}\right)\cos \frac{\pi }{2}\left[\left(2.00{\text{m}}^{-1}\right)x-\left(8.00{\text{s}}^{-1}\right)t\right].$

Calculate the (a) frequency, (b) wavelength, and (c) speed of each wave. For x ≥ 0, what is the location of the node having the (d) smallest, (e) second smallest, and (f) third smallest value of x? For x ≥ 0, what is the location of the antinode having the (g) smallest, (h) second smallest, and (i) third smallest value of x?