When Does the Wave Reach Maximum Displacement?

[kathyt.25]

Homework Statement

The displacement of the wave traveling in + x direction is: Y(x, t) = 0.35 (m) Sin (6x- 30t); where x is in meter and t is in second.

If the wave reaches its maximum displacement after 0.04 sec,
what is the value of x corresponding to y (max).

Homework Equations

Y(x,t)=Asin(kx-wt)

The Attempt at a Solution

Well I know that with a "standard" sin curve, it reaches a maximum when x=pi/2. However, doesn't this particular displacement equation Y(x, t) = 0.35 (m) Sin (6x- 30t) have a horizontal compression (ie. indicated by what's in the brackets, 6x-30t) so that it's maximum (ie. max displacement) wouldn't occur at 90 degrees on the x axis?

The answer key says that sin is at a maximum when x=pi/2
So pi/2 = 6x-30(0.04)

 

[RoyalCat]

What does multiplying a function by a constant do? Does it change how it behaves?
Also note that you get vertical compression from the constant 0.35.

Any sine function reaches its maximum when its argument equals π/2 (You can prove this by differentiating y=A*sin(t)), regardless of any phase shifts brought on by how the argument behaves, and regardless of any compression/stretching brought on by multiplying it by a constant.

I'm glad you interpreted what the answer key says right. sin(t) is at a maximum when t=π/2, not when x equals π/2, but when the entire argument does.