Halliday, Resnick & Walker — Waves-I: Problem 48

48 A sinusoidal wave is traveling on a string with speed 40 cm/s. The displacement of the particles of the string at \(x = 10 \text{ cm}\) varies with time according to \(y = (4.0 \text{ cm}) \sin[5.0 - (4.0 \text{ s}^{-1})t]\). The linear density of the string is 4.0 g/cm. What are (a) the frequency and (b) the wavelength of the wave? If the wave equation is of the form \(y(x, t) = y_m \sin(kx \pm \omega t)\), what are (c) \(y_m\), (d) \(k\), (e) \(\omega\), and (f) the correct choice of sign in front of \(\omega\)? (g) What is the tension in the string?