Home » Calculation of Phase angle − Phase Difference Phase shift

Calculation of Phase angle − Phase Difference Phase shift

Determining phase angle φ° in degrees (deg), the time delay Δ t and the
frequency
f is:

Phase angle (deg)   
(Time shift) Time difference    
Frequency   

λ = c / f  and  c = 343 m/s at 20°C.

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


Phase angle (rad)   
"Bogen" means "radians". (Time shift) Time difference
Frequency   

Time = path length / speed of sound
The difference in time length of sound for each meter

Effect of temperature on the time difference Δ t
 Temperature
of air in °C
Speed of sound
c in m/s
 Time per 1 m
Δ t in ms/m
+40354.92.818
+35352.02.840
+30349.12.864
+25346.22.888
+20 343.22.912
+15340.32.937
+10337.32.963
  +5334.32.990
  ±0331.33.017
  −5328.23.044
−10325.23.073
−15322.03.103
−20318.83.134
−25315.73.165


 Audio experts normally work with the rule of thumb:
  When distance of
r = 1 m is considered the sound demands approximately t = 3 ms in air.
 Δ t = r / c and r = Δ t × c       Speed of sound c = 343 m/s at 20°C.

When we have fixed time delay of Δ t = 0.5 ms we find
the below expressed phase shift φ° (deg) of the signal:

Phase difference
φ° (deg)
Phase difference
φBogen (rad)
 Frequency 
f
Wavelength
λ = c / f
360°  2 π = 6.283185307  2000 Hz0.171 m
180°   π = 3.141592654 1000 Hz0.343 m
   90°π / 2 = 1.570796327    500 Hz0.686 m
   45°π / 4 = 0.785398163     250 Hz1.372 m
      22.5°π / 8 = 0.392699081    125 Hz2.744 m
        11.25°π /16= 0.196349540   62.5 Hz5.488 m

Phase angle: φ° = 360 × f × Δ t       For time-based stereophony Δ t = a × sin α / c
Frequency f = φ° / 360 × Δ t

Phase angle (deg) φ = time delay Δ t × frequency f × 360
Consider the time difference Δ t = path length a / speed of sound c, then we find
Phase difference φ° = path length
a × frequency
f × 360 / speed of sound c

You must enter at least two values, the third value will be solved and presented
Phase angle (deg) φ  °
 (Time shift) time delay Δ t  ms
Frequency f  Hz
Phase shifter circuit for phase angles from φ = 0° to 180°


Although we need a constant clear frequency response, the "linear" phase demands some
elaboration.
You may see engineers expecting ideal phase as constant like the amplitude response.
That is incorrect. At the start, the phase commences at 0° due to the fact that the lowest frequency finishes at 0 Hz, at DC. (You won't find any phase angle between DC voltages).
AS it proceeds for a given frequency a phase angle is meaningless, if the phase angle is
only two times as big for a  double frequency, and thrice as significant as in triplicate, etc.

A sine wave involving 1500 Hz. frequency (period T = 0.667 ms) as well as its delayed
iteration, at 1 ms delay. The ending mixed signal has to be signal without any
amplitude, or perhaps a total termination of signal.
The phase shift for just about any frequency having a delay of 1 millisecond. 

Polarity reversal is no phase shift.

Polarity reversal (or Pol-Rev) is a phrase which is frequently mistaken for phase Ø (phi)
however entails no phase shift or time delay. Polarity change happens if we
"change the sign" of the amplitude values of a signal. Within the analog sphere this
can be carried out having an inverting amplifier, a transformer, or in a balanced line by
merely changing contacts among pins 2 and 3 (XLR plug) on a single end of
the cable. In the digital sphere, it really is carried out simply by altering almost all pluses to
negatives and the other way round in the audio-signal data flow.

middle: the 180° phase shifted signal
 as T/2 time shifted sawtooth

bottom: the b/a-polarity reversed (inverted) signal,
 mirrored on the time axis

Obviously it can be found that reversed polarity cannot be exactly like out of phase.

It really is concerning the much-discussed subject: "Phase shift vs. inverting a signal" and "phase
shift vs. time shift of a signal." The phrase phase shift is apparently described only for
mono frequency sine signals and the phase shift angle is clearly identified just for
sinusoidal amounts.

The typical Ø (phi)-button is only a polarity changer
There is absolutely no phase shifting



The Angular Frequency is ω = 2π × f
Given is the equation: y = 50 sin (5000 t)
Determine the frequency and the amplitude.
Answer: The amplitude is 50 and
ω = 5000.
So the frequency is f = 1/T = ω / 2 π = 795.77 Hz.

To use the calculator, simply enter a value.
The calculator works in both directions of the
sign.

Frequency f
Hz
 ↔ Angular Frequency ω
rad/s
ω = 2π × f                              f = ω / 2π

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