Answer
$(a)\space 9.64\space m/s$
$(b)\space y(x,t)=2.14cos(0.105x-1.017t)$
Work Step by Step
(a) Here we use the equation $V=\frac{\lambda}{T}$ , where $V$ - speed of the wave, $\lambda$ - wave length, T - period of the wave.
The 3.09 s through to crest time is half the full crest-to-crest period T, so T = 6.18s. wavelength is = 59.6 m
$V=\frac{\lambda}{T}$
$V=\frac{59.6}{6.18}=9.64\space m/s$
(b) To describe the wave with equation 14.3 we need the amplitude A, wave number K & angular frequency $\omega$
$A=\frac{4.28\space m}{2}=2.14\space m$
$K=\frac{2\pi}{\lambda}=\frac{2\pi}{59.6\space m}=0.105 m^{-1}$
$\omega=\frac{2\pi}{T}=\frac{2\pi}{6.18\space s}=1.017\space s^{-1}$
$\space y(x,t)=Acos(Kx\pm\omega t)$
$y(x,t)=2.14cos(0.105x-1.017t)$
