How fast is an ocean wave with given displacement and time function?

[forestmine]

Homework Statement

Find the speed of an ocean wave whose vertical displacement y as a function of time t is given by y(x,t) = 3.7 cos(2.2x - 5.6t), where all quantities are in SI units.

Homework Equations

v=-ωAsin(kx-ωt)

The Attempt at a Solution

I'm really not at all sure where to begin with this one. I'm not even sure if my derivative equation is correct...

Any direction at all would be much appreciated! Thank you!

 

[olivermsun]

have you been introduced to the definition of "wave speed"?

 

[forestmine]

I believe so. The wave speed is the speed at which the disturbance propagates throughout the medium...v=λf. So that's the equation I need instead?

In that case, when you take the derivative of position and are given a velocity function, what exactly is that the velocity of? The speed something travels along the wave?

 

[olivermsun]

Your function y(x,t) tells you the height of the free surface at each position and time. By taking the derivative dy/dt, you've found the (vertical) velocity of the surface as it heaves up and down, but that isn't the same thing as the speed the wave crests move horizontally as they propagate. For that you need to look carefully at the definition v=λf. What can you tell about λ and f from your original expression: y(x,t) = 3.7 cos(2.2x - 5.6t) ?

 

[forestmine]

Hm, I believe it gives me my amplitude, k, and angular frequency?

 

[forestmine]

Aha! I got it! Since it gives us k and omega, we simply use the relation omega=2*pi*f and k=(2*pi)/lambda. And then substituting in for v=f*lambda gives us our answer.

I need to keep my wave speed vs. velocity of vertical movement straight...

Thank you so much!

 

[olivermsun]

You're welcome! \o/