Instantaneous Displacement of a Sound Wave

[Mtscorpion12]

Homework Statement

A sinusoidal sound wave moves through a medium and is described by the displacement wave function s(x,t) = 2.00cos(15.7x - 858t) where s is in micrometers, x is in meters, and t is in seconds. Find a) the amplitude, b) the wavelength, and c) the speed of this wave. D) Determine the instantaneous displacement from equilibrium of the elements of the medium at the position x=0.050 m and t=3.00 ms. E) Determine the maximum speed of the element's oscillatory motion.

Homework Equations

The Attempt at a Solution

I have already figured out A, B, and C but cannot figure out D or E. I believe D is just to find the derivative and plug in the given X and T, but I do not know how to find the derivative of a three variable function. Also, I believe E just requires setting the derivative equal to 0 and finding when it is a maximum.

 

[Nathanael]

I believe D is just to find the derivative and plug in the given X and T

No need; it asks for the instantaneous displacement. The given function s(x,t) gives you the displacement at every position and every time.

Also, I believe E just requires setting the derivative equal to 0 and finding when it is a maximum.

That would give you the maximum displacement, (not the maximum speed,) but you don't even need to differentiate to find that; it's simply the amplitude.

 

[Mtscorpion12]

Clearly I overthought this problem way too much. I got it now.

Thank you very much.