Editing Phase (waves) (section)

===For sinusoids with same frequency===
For sinusoidal signals (and a few other waveforms, like square or symmetric triangular), a phase shift of 180° is equivalent to a phase shift of 0° with negation of the amplitude.  When two signals with these waveforms, same period, and opposite phases are added together, the sum <math>F+G</math> is either identically zero, or is a sinusoidal signal with the same period and phase, whose amplitude is the difference of the original amplitudes.

The phase shift of the co-sine function relative to the sine function is +90°.  It follows that, for two sinusoidal signals <math>F</math> and <math>G</math> with same frequency and amplitudes <math>A</math> and <math>B</math>, and <math>G</math> has phase shift +90° relative to <math>F</math>, the sum <math>F+G</math> is a sinusoidal signal with the same frequency, with amplitude <math>C</math> and phase shift <math>-90^\circ < \varphi < +90^\circ</math> from <math>F</math>, such that
<math display="block">C = \sqrt{A^2 + B^2} \quad\quad \text{ and } \quad\quad \sin(\varphi) = B/C.</math>

[[Image:Sine waves same phase.svg|thumb|In-phase signals]]
[[Image:Sine waves different phase.svg|thumb|Out-of-phase signals]]
[[File:Phase Comparison image two waves.gif|thumb|Representation of phase comparison.<ref name=phnist/>]]
[[Image:Phase-shift illustration.png|thumb|200px|Left: the [[real part]] of a [[plane wave]] moving from top to bottom. Right: the same wave after a central section underwent a phase shift, for example, by passing through a glass of different thickness than the other parts.]]

[[File:Out of phase AE.gif|thumb|Out of phase AE]] 
A real-world example of a sonic phase difference occurs in the [[Native American flute#The Warble|warble of a Native American flute]]. The amplitude of different [[Harmonics|harmonic components]] of same long-held note on the flute come into dominance at different points in the phase cycle.  The phase difference between the different harmonics can be observed on a [[spectrogram]] of the sound of a warbling flute.<ref>{{cite web |url=http://Flutopedia.com/warble.htm |title=The Warble |work=Flutopedia |author1=Clint Goss |author2=Barry Higgins |year=2013 |access-date=2013-03-06}}</ref>