Course:Phys341 2020/Multi-frequency sound interference

Figure 1. Constructive Interference. Two in-phase sine waves of the same amplitude being superimposed to create a sine wave with double the amplitude (Own Work using Canva)

Figure 2. Destructive Interference. Two out-of-phase sine waves of the same amplitude being superimposed to create a flat standing wave with an amplitude of zero (Own Work using Canva)

Sound interference refers to the process of sound waves becoming superimposed onto each other as to result in either partial or full destructive and constructive interference.

In most cases, when we look at literature about sound interference, we only see the mechanisms of single-frequency sound interference. With this project, I am aiming to break down the mechanism of multi-frequency sound interference and how it should be conceptually broken down. With regard to music, all types of music that we listen to contains multi-frequencies. While understanding single-frequency interference is important to learn the basic concepts, understanding the mechanism of multi-frequency interference can allow us to tweak the way we make acoustic electronic music. We can use multi-frequency interference to remove static or white noise from recordings that we've made. We can use it to understand how different tracks fit together in a song and what might interfere with other elements. We can even begin to understand the technology of noise-cancelling headphones. Understanding multi-frequency sound interference and using it intelligently allows for a vastly different way to produce and edit music!

Sound Interference Mechanisms

In the case of constructive interference, waves of the same or different amplitudes superimpose and create larger waves. This type of interference is the result of waves that superimpose while in phase with each other. In phase meaning the troughs of waves line up with troughs of the other waves, and the same for peaks lining up with other peaks. When waves are out-of-phase, superimposed waves result in partial or full destructive interference, where the portions of the waves that are out-of-phase, meaning troughs meet with crests, will cancel out. Depending on the similarity in the amplitudes of the waves and the level of displacement, they could partially cancel out, or fully cancel out to result in dead zones. A wave that is out-of-phase by 180° will resemble the exact inverse of the original wave, allowing for full destructive interference given that the amplitude is the same.

Using Ableton for Sound Production

Figure 3. Ableton wavetable synthesizer sound design (Own Work using Ableton)

For our purposes, we can use Ableton Live 10 Suite to create different types of sound waves, as well as using audio effects to imitate out-of-phase waves. Ableton is a sound production software widely used by electronic music producers and musicians to create synthesizers from scratch and mix audio. In our context, a synthesizer is not synonymous with a keyboard. Electronic or midi keyboards are simply controllers for the synth, but the synth itself is just the sound wave. The timbre of synths comes from their frequency spectrums. On Ableton, by using the wavetable instrument, you can adjust the timbre of the synth by hand. A wavetable allows you to take a simple sine wave and adjust it in any way you wish.

To briefly understand the way wavetables operate, we can break down the synth shown in figure 3. This synth is part of a short song created that we will later use to demonstrate multi-frequency destructive interference.

Figure 3 is the sound design for a handmade synth called "Wet Aer Bass." Each part of the sound design adjusts the original sine wave and thus changes the timbre of the synth. We can observe the changes in timbre that each part of the sound design causes by focusing in on one track played in the song by this synth by reverting to a basic wavetable, starting at a sine wave, and listening to each adjustments' result on the synth.

Figure 4. Sine Wave (Own Work using Ableton)

1.) The basic wet aer bass polyphonic synth emitting simple sine waves: wet aer bass sine wave.

2.) Emitting triangle waves: wet aer bass triangle wave.

3.) Emitting 30% amber waves: wet aer bass amber wave.

Amber waves are a complex wave pattern which can be found through the wavetable presets on Ableton

4.) Amber waves with reverb: wet aer bass reverb

Figure 5. Triangle Wave (Own Work using Ableton)

Figure 6. Amber Wave (Own Work using Ableton)

Reverb, or reverberation, is essentially a persistence of sound after the initial sound is emitted. In the context of our wet aer bass synth, reverb is the sound persisting after notes on the keyboard are pressed then released.

Figure 7. OTT (Own Work using Ableton)

Figure 8. OTT (Own Work using Ableton)

Figure 9. Echo (Own Work using Ableton)

5.) Amber waves with EQ audio effects and OTT: wet aer bass EQ and OTT.

EQ audio effects allow you to raise and lower certain portions of the synth's frequency spectrum. For the wet aer bass synth, middle-range frequencies are slightly lowered and both lower and higher frequencies are slightly increased to result in a brighter and more aggressive sound. Along with EQ, this synth also has an OTT filter which is an audio effect that compresses sound. OTT compression is unique in the way which it divides the frequency spectrum into high, low, and medium frequencies, and adjusts the dynamics within each of those divisions. This usage of OTT compression also results in a punchier sound.

6.) Amber waves with an Echo audio effect: wet aer bass echo.

The echo audio effect is essentially a way to put delay on tracks in Ableton. The echo effect allows you to change the level that the left speaker and right speaker line up when playing back sound while also adding delay to the sound. Delay is essentially sound being repeated after it is initially produced. In this track, the wet aer bass has an echo filter that progressively gets stronger as the track nears its finish. Meaning the left and right speakers are slightly out of line, and the delay gets stronger near the end.

Figure 10. Frequency Spectrum of Wet Aer Bass Synth playing C4 (Own Work using Spectrum Lab)

7.) Final synth: wet aer bass final

After several smaller tweaks, the final synth has a complex frequency spectrum which makes its timbre unique and much more different than the sine wave we started with. The resulting frequency spectrum is interesting to analyze. Figure 10 shows the frequency spectrum for wet aer bass playing a C4 (middle C on a keyboard.) We can see that the fundamental frequency is much softer than say, C3 or C5. Additionally, you can see the frequencies which are boosted by the OTT and EQ effects and which are nearly completely removed. Additionally, by seeing the frequency spectrum of this synth, we can anticipate the shape of the wave.

Figure 11. Multi-frequency sine wave (Own Work using Fourier Sequence)

Figure 12. Two sine waves superimposed (Own Work using Fourier Sequence)

Multi-frequency Destructive Sound Interference

Single-frequency sine waves are waves that have a single crest and trough in each wavelength. They are relatively simple to analyze and thus, in most cases, when we look at sound interference, we tend to look at single-frequency sine waves because you can see the entire wave and where it cancels out or adds together if superimposed with another single-frequency sine wave. Multi-frequency sound interference should be seen similarly. There are two different ways to analyze a multi-frequency wavelength. Either by looking at the multi-frequency wave itself or by looking at each of the separate waves, the harmonics, that are being superimposed to create the multi-frequency wave. In figures 11 and 12, there is the same wave shown in both in its multi-frequency waveform and just its harmonics respectively. Both waves sound and are essentially the same, but the first is just the superimposition of the second.

Figure 13. Wet aer bass synth wave-form (Own Work using Ableton)

The frequency spectrum of the wet aer bass synth explains the shape of its wave. Figure 13 shows the wave-form of the synth when playing C4. The wave is the result of the superimposition of the many harmonics within the frequency spectrum, which are shown in figure 10. As a result, the multi-frequency wave does not simply have one crest and trough per wavelength, but rather a complex wave-form. Since this wave is synonymous with all the harmonics which the wave is composed of superimposed together, when we are looking at multi-frequency sound interference, we should think of the waves as just that, the harmonics being superimposed together rather than the multi-frequency wave shown similar to that which is shown in figure 11. If the wave in figure 12 is played out of one sound source and the inverse of just the orange (shorter) wave in figure 12 is played out of a secondary sound source, in the spots where the waves meet, the orange waves will be perfectly out-of-phase with the same amplitude, and the result will not be a dead zone like it would be when single-frequency waves interfere. The result would be just the red wave being emitted and the orange waves cancelling out.

To observe multi-frequency sound interference, we can experiment with destructive sound interference using this short song as our sample. The goal of the sound interference experiment will be to see how two sound sources out-of-phase will interact. Out of one sound source, every frequency found in the song will be played at the same time, for the entire duration of the song. The song will be notated and we can create an exact opposite of this notation which will contain every frequency found in the song played constantly except for whenever its actually supposed to play. Out of the second sound source, we can play this opposite version of the song. The result would be, wherever the waves met out-of-phase, 'everything' would cancel out with 'everything except the song' and only the song would be emitted in the places that these waves cancel out.

Figure 14. Sine wave and its out-of-phase counterpart (Own Work using Ableton)

Using Ableton to Imitate Destructive Sound Interference

To observe sound interference, waves need to be emitted in spaces with very limited to no reflective surfaces. Destructive sound interference can not be easily observed in spaces with reflections since you would not be able to analyze spots where out-of-phase waves would create dead zones. However, you would be able to observe this phenomenon in open fields or in special rooms built to limit sound reflections, such as anechoic chambers. Although, without access to these spaces or the equipment required to observe this process happen, the next best way to imitate destructive sound interference is to use sound production software to imitate waves meeting out-of-phase. After using Ableton to create our own synths and waves, we are able to have a full grasp on what frequencies are in our song and when they play. Now we can use the software to mimic out-of-phase waves. Ableton contains an audio effect called "utility" which allows you to make the inverse of waves, essentially making them 180° out-of-phase.

Using this feature, we can observe destructive sound interference in different types of waves. All of the following are waves being played, then the inverse, then both together.

1.) Single-frequency sine waves

2.) Single-frequency square waves

All of the following are multi-frequency waves being played, then the inverse of some of the harmonics found in the original wave, then both together (a triad, an interval, then both).

1.) Multi-frequency sine waves

2.) Multi-frequency square waves

Now we can test out the destructive sound interference of individual tracks within the song. All of the following are the individual track being played, then all of the frequencies within the track, then all the frequencies except the song played out-of-phase, then the latter two played together.

1.) Synth 1

2.) Synth 2

3.) Synth 3

Finally, we can test the destructive interference of the entire song. The following is a short clip of the intro, then every frequency, then all the frequencies except the song played out-of-phase, then the latter two played together. In some of these sound files, we can hear white noise which we shouldn't be hearing if the cancellation is happening properly. These problems can most likely be attributed to exporting problems on Ableton and audacity, or uploading problems to wiki. In theory, multi-frequency waves are the same as many single-frequency waves superimposed. So when these waves meet with other waves which are 180° out-of-phase, they should cancel out fully given the amplitudes are the same. If certain harmonics are left not inversed, they will play through, as shown in the above demos.