Halliday, Resnick & Walker — Waves–I: Problem Problem_23

A sinusoidal transverse wave is traveling along a string in the negative direction of an x axis. Figure 16.12 shows a plot of the displacement as a function of position at time \( t = 0 \); the scale of the y axis is set by \( y_s = 4.0 \text{ cm} \). The string tension is \( 3.6 \text{ N} \), and its linear density is \( 25 \text{ g/m} \). Find the (a) amplitude, (b) wavelength, (c) wave speed, and (d) period of the wave. (e) Find the maximum transverse speed of a particle in the string. If the wave is of the form \( y(x, t) = y_m \sin(kx \pm \omega t + \phi) \), what are (f) \( k \), (g) \( \omega \), (h) \( \phi \), and (i) the correct choice of sign in front of \( \omega \)?