Answer
We can write the equation for this wave:
$y(x,t) = (2.50~cm)~sin~[~(8.0~rad/m)~x - (2.90~rad/s)~t~]$
Work Step by Step
The maximum speed of a point on the string is $v_m = A~\omega$. Then the wave speed is $5A\omega$. We can find the wave number $k$:
$v = \frac{\omega}{k}$
$k = \frac{\omega}{v}$
$k = \frac{\omega}{5~A~\omega}$
$k = \frac{1}{5~A}$
$k = \frac{1}{(5)(0.0250~m)}$
$k = 8.0~rad/m$
In general: $y(x,t) = A~sin(k~x-\omega~t)$
We can write the equation for this wave:
$y(x,t) = (2.50~cm)~sin~[~(8.0~rad/m)~x - (2.90~rad/s)~t~]$
