Waves on water

  • Thread starter asaspades
  • Start date
  • #1
12
0

Homework Statement



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

Homework Equations



[itex]\omega = 2\pi f[/itex]
[itex]k=\frac{2\pi}{\lambda}[/itex]

The Attempt at a Solution



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

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:

Answers and Replies

  • #2
haruspex
Science Advisor
Homework Helper
Insights Author
Gold Member
34,550
5,966
Your error is in converting 0.450cm−1 to m-1. You've handled it as though converting from cm to m.
 

Related Threads on Waves on water

  • Last Post
Replies
4
Views
2K
  • Last Post
Replies
3
Views
1K
  • Last Post
Replies
2
Views
2K
  • Last Post
Replies
6
Views
5K
  • Last Post
Replies
2
Views
928
  • Last Post
Replies
8
Views
1K
  • Last Post
Replies
1
Views
2K
  • Last Post
Replies
4
Views
12K
  • Last Post
Replies
1
Views
2K
  • Last Post
Replies
2
Views
4K
Top