Halliday, Resnick & Walker — Waves–I: Problem Problem_57

A generator at one end of a very long string creates a wave given by \[ y = (6.0 \text{ cm}) \cos \frac{\pi}{2} [(2.00 \text{ m}^{-1})x + (8.00 \text{ s}^{-1})t], \] and a generator at the other end creates the wave \[ y = (6.0 \text{ cm}) \cos \frac{\pi}{2} [(2.00 \text{ m}^{-1})x - (8.00 \text{ s}^{-1})t]. \] Calculate the (a) frequency, (b) wavelength, and (c) speed of each wave. For \( x \ge 0 \), what is the location of the node having the (d) smallest, (e) second smallest, and (f) third smallest value of \( x \)? For \( x \ge 0 \), what is the location of the antinode having the (g) smallest, (h) second smallest, and (i) third smallest value of \( x \)?