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Section angle calculation time delay frequency calculate section lag time shift between voltage distinction time of arrival ITD oscilloscope measure two indicators formulation angle present voltage phi section shift time distinction

Section angle calculation time delay frequency calculate section lag time shift between voltage distinction time of arrival ITD oscilloscope measure two indicators formulation angle present voltage phi section shift time distinction

2023-08-10 10:42:16

Section angle calculation time delay frequency calculate section lag time shift between voltage distinction time of arrival ITD oscilloscope measure two indicators formulation angle present voltage phi section shift time distinction – sengpielaudio Sengpiel Berlin

Phase angle, time delay and frequency formula angle current voltage phi phase between voltage oscilloscope measure two signals phase lag time shift time difference - sengpielaudio





Query: What’s the formulation for the section of a sine wave?

There isn’t a section of a sine wave. A sine wave has no section.

A section can solely develop between two sine waves.

Two sine waves are mutually shifted in section, if the time factors

of its zero passages don’t coincide.



The phrase section has a transparent definition for 2 pure touring AC sinusoidal waves,

however not for music indicators.
All equalizers shift section with frequency. With none

fixed-point no “shifting” (displacement) is feasible.

Particular methods:
90° filter with two allpass filters. Phases are at all times section variations.


Polarity reversal (pol-rev) is rarely phase shift on the time axis t.


Sinusoidal waveforms of the identical frequency can have a section distinction.


If there’s a section shift (section distinction) or section delay of the phase angle φ

(Greek letter Phi) in levels it needs to be specified between which
pure signals

(sine waves) this seems. Thus, for instance, a section shift could be between the 2 stereo

channel indicators left and proper, between the enter and output sign, between voltage and

present, or between sound strain p and velocity of the air particles

What is actually an amplitude?

Sinosoidial Wave


One full cycle of the wave is related to an “angular” displacement of

π radians.               omega


The section φ is the angle of a sign portion, it’s laid out in angular levels and

offers a reference to the reference worth of the whole sign. For periodic indicators is the

complete section angle of 360 levels and a interval equal to the interval length.

A typical query: What’s the frequency and the section angle of a sinusoidal waveform?

Does “one” sign can actually have a section?

Two “in-phase” waves have a section (angle) of φ = 0 levels.

If the frequency = 0 Hz, then there isn’t any AC voltage – that is simply DC. Then there will probably be no

section angle current.

What has time delay to do with section angle?

The time distinction (length) of sound per meter


Impact of temperature on the time distinction Δ t

Dependence of the speed of sound solely on the temperature of the air


of air in °C
Pace of sound

c in m/s
 Time per 1 m 

Δ t in ms/m
+40 354.9 2.818
+35 352.0 2.840
+30 349.1 2.864
+25 346.2 2.888
+20  343.2 2.912
+15 340.3 2.937
+10 337.3 2.963
  +5 334.3 2.990
  ±0 331.3 3.017
  −5 328.2 3.044
−10 325.2 3.073
−15 322.0 3.103
−20 318.8 3.134
−25 315.7 3.165



 Sound engineers take often the rule of thumb:

 For the gap of
r = 1 m the sound wants about t = 3 ms in air.

 Δ t = r / c and r = Δ t × c       Pace of sound c = 343 m/s at 20°C.



For a fastened time delay of Δ t = 0.5 ms we get

the next section shift φ° (deg) of the sign:


Section distinction

φ° (deg)
Section distinction

φBogen (rad)


λ = c / f
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

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

Frequency f = φ° / 360 × Δ t

Section angle (deg) φ = time delay Δ t × frequency f × 360

When you take the time distinction Δ t = path size a / pace of sound c, then we get

Section distinction φ° = path size
a × frequency
f × 360 / pace of sound c

Please enter two values, the third worth will probably be calculated

Some extra assist: Time, Frequency, Phase and Delay

By Lord Rayleigh
(John William Strutt, third Lord Rayleigh, 1907) the duplex theory

was proven. This concept contributes to understanding the process of “pure

listening to” with people. It’s the quite simple realization that the interaural time of arrival

variations ITD are essential at frequencies beneath 800 Hz as
phase differences

with the localization direction as ear signals, whereas at frequencies above 1600 Hz

solely the interaural degree variations ILD are efficient.

Between the ears the utmost delay quantities to 0.63 ms. Section variations for

particular person frequencies could be calculated.

Section shifter circuit for section angles from φ = 0° to 180°


Voltage vectors of the section shifter

Phase shifter circuit        Voltage vectors

For R = 0 ohm is VOUT = VIN. The output shouldn’t be loaded by low impedance.

You’ll be able to shift single pure frequencies (sine waves),

however that’s inconceivable with this schematics for music applications.

See Also

Two sine voltages – section shifted: φ = 45°

45° phase shifted

Circumstances for distortion-free transmission

From Schoeps – Joerg Wuttke: “Mikrofonbuch” – Chapter 7

The Phase


Whereas the demand for a continuing frequency response is evident, the “linear” section wants slightly


There are engineers who anticipate the best section as fixed just like the amplitude response.

That’s not true. Initially, the section begins at 0° as a result of the bottom frequency ends at 0 Hz, at

DC. (There isn’t a section angle between DC voltages).

Within the course at a given frequency a section angle is with out which means, if the section angle is

solely twice as massive within the case of double frequency, and 3 times as massive in triplicate, and many others.

Courtesy of David Moulton Laboratories

(About Comb Filtering, Section Shift and Polarity Reversal)

Delay line

Digital equal of the movement of a sign and its delayed iteration, recombined right into a

single sign. Within the case we will probably be , the delay line has a delay of 1 millisecond,

the degrees of each the unique and delayed indicators going into the mixer are equal, and the

sign is a 1 kHz sine wave.

Delayed signal

A sine wave of 1500 Hz. frequency (interval T = 0.667 ms) and its delayed

iteration, at 1 ms delay. The ensuing combined sign will probably be a sign with no

amplitude, or an entire cancellation of sign.

Phase Shift


The section shift for any frequency with a delay of 1 millisecond. The diagonal line

represents the rising section shift as a operate of frequency. Be aware that we will

consider 540° as being successfully the identical as 180°.

Time, Phase, Frequency, Delay – An audio signal theory primer/refresher

Polarity reversal is not any Phase shift of 180° (time delay)

Ø (phi) = section shift, section shifting, section distinction, displacement of section,

section lag, section angle are sometimes not appropriate used as:pol-rev = polarity reversal.



Polarity and section are sometimes used as in the event that they imply the identical factor. They aren’t.

The “section reverse button” doesn’t change the section. It reverses the polarity.

Polarity reversal is not any section shift.

Polarity reversal (or Pol-Rev) is a time period that’s typically confused with section Ø (phi)

however entails no section shift or time delay. Polarity reversal happens at any time when we

“change the signal” of the amplitude values of a sign. Within the analog realm this

could be carried out with an inverting amplifier, a transformer, or in a balanced line by

merely switching connections between pins 2 and three (XLR plug) on one finish of

the cable. Within the digital realm, it’s carried out by merely altering all pluses to

minuses and vice versa within the audio-signal information stream.

Two sawtooth oscillations

Polarity reversed signal  prime: the authentic sign a/b (noticed tooth)


 center: the 180° section shifted sign

 as T/2 time shifted sawtooth


 backside: the b/a-polarity reversed (inverted) sign,

 mirrored on the time axis


Clearly could be seen that reversed polarity can’t be the identical as out of section.


It’s concerning the much-discussed matter: “Section shift vs. inverting a sign” and “section

shift vs. time shift of a sign.” The time period section shift is supposedly outlined just for

mono frequency sine indicators and the section shift angle is explicitly outlined just for

sinusoidal portions.

The everyday Ø (phi)-button is just a polarity changer

There’s completely no section shifting

Polarity reversal



Be aware: Time, frequency and section belong shut collectively.

The peak of the amplitude has no affect on these parameters.



The Angular Frequency is ω = 2π × f

Given is the equation: y = 50 sin (5000 t)

Decide the frequency and the amplitude.

Reply: The amplitude is 50 and
ω = 5000.

So the frequency is f = 1/T = ω / 2 π = 795.77 Hz.

To make use of the calculator, merely enter a worth.

The calculator works in each instructions of the


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