Walker, Halliday & Resnick — Waves-I: Problem 42

42 The equation of a transverse wave traveling along a very long string is \(y = 3.0 \sin(0.020\pi x - 4.0\pi t)\), where \(x\) and \(y\) are expressed in centimeters and \(t\) is in seconds. Determine (a) the amplitude, (b) the wavelength, (c) the frequency, (d) the speed, (e) the direction of propagation of the wave, and (f) the maximum transverse speed of a particle in the string. (g) What is the transverse displacement at \(x = 3.5 \text{ cm}\) when \(t = 0.26 \text{ s}\)?