I'm trying to understand the principle of active noise control, a technique to reduce noise by using interference. Wikipedia says:
A noise-cancellation speaker emits a sound wave with the same amplitude but with inverted phase (also known as antiphase) to the original sound. The waves combine to form a new wave, in a process called interference, and effectively cancel each other out – an effect which is called destructive interference.
This simple explantion makes perfect sense to me except one thing — what exactly is "antiphase"?
If we are talking about pure sinusoidal sound waves, then it is pretty simple. Two waves with a phase difference of 180˚ are in antiphase, and if their amplitudes are the same, they will interfere with each other and cancel each other.
My question arises when talking about non-sinusoidal periodic waves. In order to cancel such a wave
F(t), we need an inverted wave with the same amplitude, i.e.
-F(t). But now, because it is not a sinusoidal curve, this inverted wave
-F(t) is not identical to the phase-shifted original wave by 180˚
L is the cycle length of
F(t). Can we still call this inverted wave
-F(t) as "antiphase"? Isn't it literally an inverted in-phase wave (because we haven't changed the phase at all)?