Phase angle, time delay and frequency - sengpielaudio
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Calculation of phase angle (phase difference) from
time delay (time of arrival ITD) and frequency
Connection between phase, phase angle, frequency and time of arrival Δ t (delay)

The word phase has a clear definition for pure traveling sinusoidal waves, but not for music signals. All equalizers shift phase, unless it uses very special tricks. Phases are always phase differences.
Polarity reversal (pol-rev) is not phase shift on the time axis t.

If there is a phase shift of the phase angle in degrees it has to be specified between which pure signals (sinus) it appears. Thus, for example, a phase shift can be between the stereo signals left and right, between the input and output signal, between voltage and current, or between sound pressure p and velocity v of the air particles.
Sinosoidial Wave
One complete cycle of the wave is associated with an "angular" displacement of
2 π radians.               omega

What has time delay to do with phase angle?

frequency f   Hz
time delay Δ t   ms
   
   
phase difference φ in degrees   ° or deg
φ in radians    rad
wavelength λ   m
Calculation between phase angle φ° in degrees (deg), the time delay Δ t and the frequency f is:

Phase angle (deg)   Phase-Laufzeit

Time difference    Laufzeit-Phase

Frequency   Frequenz-Phase

λ = c / f and c = 343 m/s at 20°C.

Calculation between phase angle φ in radians (rad), the time delay Δ t, and the frequency f is:

Phase angle (rad)   Bogen-Laufzeit

"Bogen" means "radians".

Time difference    Laufzeit-Bogenwinkel

Frequency   Frequenz-Bogenwinkel

For a fixed time delay of Δ t = 0.5 ms we get
the following phase shift φ° (deg) of the frequency:

Phase difference
φ° (deg)		 Phase difference
φBogen (rad)		 Frequency
f		 Wavelength
λ
360°   2 π = 6.283185307 2000 Hz 0.171 m 
180°      π = 3.141592654 1000 Hz 0.343 m
   90° π / 2 = 1.570796327   500 Hz 0.686 m
   45° π / 4 = 0.785398163   250 Hz 1.372 m
       22.5° π / 8 = 0.392699081   125 Hz 2.744 m
         11.25° π /16= 0.196349540   62.5 Hz  5.488 m

Conversion: radians to degrees and vice versa

Phase angle (deg) φ = delay Δ t × frequency f × 360
Please enter two values, the third value will be calculated

phase angle (deg) φ:  ° Magisches Dreieck Ohm
time delay Δ t:  ms
frequency f:  Hz

Some more help: Time, Frequency, Phase and Delay

By Lord Rayleigh (John William Strutt, 3rd Lord Rayleigh, also Raleigh, 1907) the duplex theory was shown. This theory contributes to understanding the procedure of "natural hearing" with humans. It is the very simple realization that the interaural time of arrival differences ITD are important at frequencies below 800 Hz as phase differences with the direction localization as ear signals, while at frequencies above 1600 Hz only the interaural level differences ILD are effective. Between the ears the maximum delay amounts to 0.63 ms. The phase differences for individual frequencies can be calculated.

Phase shifter circuit for phase angles from φ = 0° to 180°

Voltage vectors of the phase shifter

Phase shifter circuit        Voltage vectors

For R = 0 ohm isVOUT = VIN. The output should not be loaded by low impedance.

You can shift single pure frequencies (sines), but that is impossible for music programs.

Two sine voltages - phase shifted: φ = 45°

45° phase shifted

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