Question

A water wave traveling in a straight line on a lake is described by the equation.

$y(x,t)=3.75cmcos(0.450c{m}^{-1}x+5.40s^{-1}t)$

where y is the displacement perpendicular to the undisturbed surface of the lake. How much time does it take for one complete wave pattern to go past a fisherman in a boat at anchor?

• A. 1.16s
• B. 3.48s
• C. 2.32s
• D. 4.64s

Answer 1

The correct option is A

1.16s

on comparing the equation to

$y=Asin(kx\pm \omega t+\varphi )$

We get $\omega =5.40s^{-1}$

The time required for one complete wave to go part the fisherman, since the fisherman is at rest, is one time period.

$T=\frac{2\pi }{\omega }=\frac{2\times 3.14}{5.4}=1.16s$

A full wave takes 1.16 s to go past the fisherman.