Problem 13.10

13.10 a)
**fig**

b)
$k = \frac{2\pi}{\lambda}$
k = 18.0 rad/m
$T = \frac{1}{f}$
T = 0.0833 s
$\omega = 2\pi f$
$\omega = 75.4 rad/s$
$\vert v\vert = f\lambda$
|v| = 4.20 m/s

c)
$y(x,t) = A \sin (kx + \omega t + \phi)$
Here, we have
$y(x,t) = .02 \sin (18 x + 75.4 t - \phi) m$
at x = 0 and t = 0, we know that y = -0.03 m, so
$-.03 = .2 \sin (-\phi)$
$\phi = .151 rad$
so, plugging it all together, we have
$y(x,t) = .02 \sin (18 x + 75.4 t - .151) m$