# Waves on water

1. Jan 10, 2014

### asaspades

1. The problem statement, all variables and given/known data

A water wave traveling in a straight line on a lake is described by the equation
$y(x,t)=(3.75\,\text{cm})\cos(0.450\,\text{cm}^{-1}x+5.40\,\text{s}^{−1}t)$
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?

What horizontal distance does the wave crest travel in that time?
2. Relevant equations

$\omega = 2\pi f$
$k=\frac{2\pi}{\lambda}$

3. The attempt at a solution

This is part of an online test we were asked to submit. For the first part I got $t=1.16\,\text{s}$ which was correct. For the second part I got the wavelength as the answer, $\lambda = \frac{2\pi}{0.0045} \approx 1396\,\text{m}$. However, the online assessment tells me that the correct answer is $0.140\,\text{m}$.

Can anyone explain where I went wrong?

(This is also question 15.10 in University Physics with Modern Physics International Edition, 13th Edition, if anyone should happen to have the solution manual to such a thing)

Last edited: Jan 10, 2014
2. Jan 10, 2014

### haruspex

Your error is in converting 0.450cm−1 to m-1. You've handled it as though converting from cm to m.

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