Answer
(a) $0.15m$
(b) $\lambda=0.10m$
(c) $24s$
(d) $4.7\times 10^{-3}m/s$
(e) toward the right
Work Step by Step
(a) We compare the given wave equation $y=15cm \space cos(\frac{\pi}{5.0cm}-\frac{\pi}{12s}t)$
with $y(x,t)=Acos(\frac{2\pi}{\lambda}-\frac{2\pi}{T}t)$ and obtain $A=15cm=0.15m$
(b) We compare the given wave equation $y=15cm \space cos(\frac{\pi}{5.0cm}-\frac{\pi}{12s}t)$
with $y(x,t)=Acos(\frac{2\pi}{\lambda}-\frac{2\pi}{T}t)$ and obtain $\frac{\lambda}{2}=5.0cm$
$\implies \lambda=10.0cm=0.10m$
(c) We compare the given wave equation $y=15cm \space cos(\frac{\pi}{5.0cm}-\frac{\pi}{12s}t)$
with $y(x,t)=Acos(\frac{2\pi}{\lambda}-\frac{2\pi}{T}t)$ and obtain $\frac{T}{2}=12s$
$\implies T=24s$
(d) We can determine the required speed as follows:
$v=\frac{\lambda}{T}$
We plug in the known values to obtain:
$v=\frac{0.10m}{24s}$
$v=4.17\times 10^{-3}m/s$
(e) We know that the wavelength is traveling to the right.
