Is PHASE constant for periodic waves?

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Is PHASE constant for periodic waves?

Post by Seismic101 »

Hi everyone - I am having "fun" with Fourier transforms this week, but I stumbled upon this question. I drew a signal (S) using the formula S(t)=A*cos(2*pi*f*t+p) where:
A = Amplitude (constant)
f= Frequency (constant)
t= Time (changing)
p= Phase

My question is about Phase. Is the phase constant for periodic waves like this Cosine wave? I used *one* value in the equation above & that's what made me think phase is constant. However, when I saw examples of phase spectra of periodic waves I noticed that phase actually changes.

My conclusion, so far, is that "phase" is not constant. Each point on the wave has its own phase, but points at equivalent locations (i.e. one cycle apart) have the same phase. The value 'p' in the equation above is actually the so called 'phase shift' because it shifts the entire waveform forward or backward. Is this accurate? Please correct me.

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Re: Is PHASE constant for periodic waves?

Post by GuyM »

You are correct, in that at any point in time you can describe the phase of a constant sinusoidal wave, but over time, that phase is varying.
See :

However the common use of the word "phase" when dealing with more complicated signals is effectively "phase difference" - the relative position of different waves relative to each other at a given time point (usually time zero)

When we split a complex signal up using Fourier analysis, you decompose it into different frequencies.
For each frequency, we have an amplitude (the strength of that frequency component) and a phase that describes the relative phase of each component at time zero.

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