Am I overthinking this? (Noise cancelling headphones for airplane noise)

[Thickmax]

Homework Statement

Am I over thinking this question

Relevant Equations

See below (shown in the question)

Can I just shift the wave over by 2Pi to get the opposite wave?

 

[haruspex]

Homework Statement:: Am I over thinking this question
Relevant Equations:: See below (shown in the question)

Can I just shift the wave over by 2Pi to get the opposite wave?

How will a shift of 2pi give you anything different from the original wave?

 

[Thickmax]

How will a shift of 2pi give you anything different from the original wave?

Shift it by 1pi then?

 

[Thickmax]

Shift it by 1pi then?

Pi/2?

 

[Gordianus]

I'd suggest drawing s(t), s_headphones and their sum.

 

[haruspex]

Shift it by 1pi then?

Pi/2?

Don't just guess. Figure it out.

 

[Thickmax]

the answer is negative the same equation...start points and end points will be the same?

Shifting the wave will move the start and end points by either (2pi, pi or pi/2)

 

[Gordianus]

I repeat my original hint: draw s(t) and s_head(t) (3, 4 of them?) and add. One of them should be close to zero.

 

[haruspex]

the answer is negative the same equation

Right, so that is a valid answer to the question.

Shifting the wave will move the start and end points by either (2pi, pi or pi/2)

Not sure what you mean by that. The equation does not have endpoints. It expresses the amplitude for all times and all locations.
If you mean shifting the entire wave, yes, there is a phase shift that is exactly equivalent to negating the expression: $\sin(\theta)=-\sin(\theta+\phi)$ for some $\phi$. You really should be able to say immediately what that value is! Consider the sines of 0°, 90°, 180°, 270°, 360°.

There is one other error in your attempt in post #1. It tells you which variables are allowed in the answer, but you have used one not in the list.