Halliday, Resnick & Walker — Waves–I: Problem Problem_64

The equation of a transverse wave traveling along a string is \(y = 0.15 \sin(0.79x - 13t)\), in which \(x\) and \(y\) are in meters and \(t\) is in seconds. (a) What is the displacement \(y\) at \(x = 2.3 \text{ m}, t = 0.16 \text{ s}\)? A second wave is to be added to the first wave to produce standing waves on the string. If the second wave is of the form \(y(x, t) = y_m \sin(kx \pm \omega t)\), what are (b) \(y_m\), (c) \(k\), (d) \(\omega\), and (e) the correct choice of sign in front of \(\omega\) for this second wave? (f) What is the displacement of the resultant standing wave at \(x = 2.3 \text{ m}, t = 0.16 \text{ s}\)?