Walker, Halliday & Resnick — Waves-I: Problem 59

59 A string oscillates according to the equation \[ y' = (0.80 \text{ cm}) \sin\left[ \left( \frac{\pi}{3} \text{ cm}^{-1} \right) x \right] \cos[(40\pi \text{ s}^{-1})t]. \] What are (a) amplitude and (b) speed of the two waves (identical except for direction of travel) whose superposition gives this oscillation? (c) What is the distance between nodes? (d) What is the transverse speed of a particle of the string at the position \( x = 2.1 \text{ cm} \) when \( t = 0.50 \text{ s} \)?