How to Find Instantaneous Displacement in a Sinusoidal Wave?

[bolivartech]

Homework Statement

A sinusoidal sound wave is described by the displacement wave function

s(x,t)=(2.00 μm)cos⁡[(15.7 m^(-1) )x-(858 s^(-1) )t]

b) Determine the instantaneous displacement from equilibrium of the elements of air at the position x = 0.050 m at t = 3.00 ms

Homework Equations

The Attempt at a Solution

s (x,t)=(2.00 μm)  cos⁡[(15.7 m^(-1) )(0.050m)-(858 s^(-1) )(.003 s) ]

Why is this this not correct?

 

[rl.bhat]

Your substitutions are correct.
What is s = ?

 

[bolivartech]

s = 3ms
the answer is supposed to be -.433 μm

 

[rl.bhat]

When you simplify the terms inside the bracket, you get 1.789 rad. To find the cos of this, either change the mode in your calculator to RAD or convert 1.789 rad to degrees and then solve for s.