Real Audio Signals
Sine waves are easy to look at to dramatically show the difference between polarity and phase. Armed with this knowledge you can look at figures 13 through 18 that show something like a real audio signal where the effects of polarity and phase are more difficult to see.
The signal shown in these figures was a generated by a mathematical algorithm that produces something close to a pink noise signal. Pink noise contains all frequencies with an equal amount of energy in each octave band. Real audio signals don’t look much different than pink noise (but one would hope they sound better!). The scales on these graphs are arbitrary. You can look at the vertical scales as +/-3 volts if you like. However, because of the way the signal was generated, there was no way to define absolute time or degrees along the horizontal scales. Suffice it to say that the phase-shifted signal used in these figures was shifted by one data point out of the 240 data points that make up the signal lines.
There is one important thing to understand about phase shift. The amount of time one signal is delayed from another will have different effects at different frequencies. Assume there is a 1 millisecond time difference between two identical signals. At 500 Hz the result will be as shown in figure 10 because at 500 Hz the 1 millisecond time difference is a phase shift of 180 degrees. The signals are offset by 1/2 a cycle.
At 1 kHz the signals will be offset by 1 complete cycle. In other words you would hear one cycle from the first signal then both combine then you’d hear the one cycle from the second signal after the first stopped. This is similar to what is shown in figure 12 (which shows only 1/2 cycle) but is not the result of the same conditions that were used to make figure 12.
At 250 Hz the effect would be as shown in figure 6 because a 1 millisecond time difference corresponds to a 90 degree phase shift at 250 Hz or an offset of 1/4 cycle. At lower frequencies the phase shift would be even less and the signals would tend to add as in figure 2, approaching but never quite reaching the 6 dB increase shown in that figure.
Contrary to phase, polarity affects all frequencies the same way. It makes the positive portions negative and the negative portions positive. Put another way, it simply flips the signal over the same way at all frequencies. With these things in mind, examine figures 12 through 18
Effects of Polarity and Phase On “Real” Audio Signals
Figure 13: This shows a pink noise signal generated as noted above.
Figure 14: This shows both the original signal in blue and what happens when an identical but phase shifted signal is added to it, as shown in red. The red signal is similar to the combined signal shown in figure 6. Note the increases in signal level and the changes in the waveform (many glitches). However you can also see the combined signal follows the original fairly closely.
Figure 15: This shows both the original signal in blue and what happens when the phase shifted signal is also reversed in polarity and combined with it, as shown in red. In this case there are huge differences between the original and combined signal.
Figure 16: To better understand what is going on, this figure shows an averaged or integrated version of the pink noise signal in figure 13. This is basically what would you would see if you graphed the readings from a typical SPL meter for the signal in figure 13.
Figure 17: This shows the averaged signal from figure 16, in blue, and the averaged combined signal from figure 14, in red. Note that there are primarily level differences (mostly increases). Otherwise the two lines look very similar.
Figure 18: This really shows what is going on in figure 15. The blue line is the averaged signal from figure 16. The red line is the averaged signal from figure 15. The red line shows that the out of polarity and phase-shifted signal approaches a straight line. Because you are looking at a broad frequency range, you are seeing a severe cancellation of the lower frequencies due to the polarity reversal. However, unlike the low frequencies, the upper frequencies do not completely cancel due to the phase shift. The red line contains primarily high frequency energy. In the blue signal the higher frequencies are the small “bumps”. These can be clearly seen in the red signal and most of them correspond to those in the blue signal.
Figure 18 is a prime example of what you would hear if you stand exactly between two speakers playing the same signal (i.e. mono) with one speaker out of polarity. The bass will disappear. But, there will always be a difference in distance between you and the speakers due to the spacing of your two ears and probably a slight overall difference in distance between you and each speaker. A difference in distance means a difference in the time arrival and thus there will be phase shifts between the sound from the two speakers. The amount of shift will vary with frequency. Because of the shorter wavelengths at high frequencies, the phase shifts allow most of the highs to be heard. They may be out of polarity but the effect is like what is shown in figure 8. Also, in a room you would also hear sound reflections from the floor, walls, and ceiling. You would only hear something like the red line in figure 18 outdoors away from any reflective surfaces or in an anechoic chamber.
The small distance between your ears and any small difference in distance from you to each speaker do not cause appreciable phase shifts at low frequencies. This is because of the considerably larger wavelengths. The difference in your distance from each speaker might be only 1 inch (25 mm). However, the wavelength of even a 1 kHz sound is roughly 1 foot (300 mm) and at 100 Hz roughly 10 feet (3 m). At the lower frequencies the polarity difference predominates because the phase shifts due to the difference in your distance from the speakers is very small compared to the wavelengths of the low frequencies. Thus the lower frequency signals, being nearly in phase but out of polarity, will cancel like in figure 4. The lower the frequency the less the phase shift between the two speakers and the greater the cancellation.
A Polarity / Phase Field Trip!!
(As with all physical exercise, check with your doctor first, who might not recommend you do this for some reason.)
Find two railroad tracks, lie across them, and wait.
Two trains, one on each track, come along. Both are right side up and both hit you at exactly the same time. The trains are in polarity and in phase.
The same thing happens again and both trains hit you at exactly the same time. However, this time one train is upside down. That is a polarity reversal.
The third time both trains are right side up but one hits you first and the other hits you shortly after the first. That is a phase shift.
The last time the second train is upside down and hits you later than the first. That is both a polarity reversal and a phase shift.
So there you have it. Although this has only touched on a few areas concerning phase and polarity issues, it is hoped you better understand the difference between the two and a few of the effects of each. Remember that the audio frequency range covers wavelengths of over 30 feet (10 meters) at the lowest frequencies to less than an inch (under 25 mm) at the highest frequencies.
While a reversal of polarity will affect all frequencies identically, a difference in time arrival between two otherwise identical signals will have very different effects on the phase between them. The amount of phase shift will be different at different frequencies and this will depend on how much time difference there is between the arrival of the two signals.