# Acoustics Part 3

## Superposition

Superposition occurs when two acoustic waves propagate simultaneously in the same sound field.

In nature, often we can observe superposition of acoustic waves due to the reason that in many cases we have distribution of more than one sound wave at the same time in the same acoustic environment.

In such a case is valid the principle of the superposition, according to which the amplitude of each point in the environment is the geometric sum of the amplitudes of all waves acting in that point at this time. Ie it is a resultant value.

In those circumstances it can be said that in applying the principle of superposition the waves pass freely through each other without changing their characteristics when making mutual interference. The result of superimposition at any point in the medium depends on the ratio between the frequencies, amplitudes and phase positions of the participating in the process, sound waves.

## Interference

What happens when we have interference between the so-called coherent sound sources?

Under coherent sources we understand two acoustic waves having the same magnitude, frequency, direction and with a constant phase displacement, as in the illustration. This is a phenomenon which frequently occurs in the various waves in nature. Analogue to this case would be simultaneous transmission of the same sound from two speakers spaced apart from each other and oriented in the same direction.

In some places the amplitude of the sources is summed and there the sound increases its strength, while in other places they are destroyed each

other.

In the first case we are talking about constructive interference, and in the other – for destructive.

The moments of aggregation and destruction depend on the length of the sound wave and the distance between the sound sources.

This is why often when we displace slightly in  the horizontal line from so-called. sweet spot between the speakers, to receive some increase in certain frequencies and attenuation in others. Practically only in the sweet spot all frequencies always arrive in the same phase, and this problem is not present.

## Beating

When we have a interference between two waves having slightly different frequencies, there  is obtained periodically an amplification and attenuation of the sound.

This effect is a frequency difference between the two frequencies, and is called the beating.

For example, if we have two frequencies – one 500 Hz, and the other – 440 Hz. The diff frequency would be 60 Hz.

We can observe in the strings of the piano, when they are just set.

Beating sometimes used when you set up musical instruments. When no beat, unisonat between the two sounds is accurate.

The beating can be heard in a relatively wide range of diff frequencies – up to about 130 Hz.

## Combinational tones

When diff frequency is in a the frequency range we can hear, it can actually be heard like a tone, although it is virtually non-existent. It is the modulated signal from the two sounds, as shown by the illustration.

If the lower frequency is f1, and higher – f2, then we hear the difference f2-f1.

There are other tones diff, in which one of the two frequencies is multiplied by 2, 3 or more. Thus may be prepared tones, a combination of:

we call combinational tones.

As we can see, the combination tones can be as diff and summary.

Their occurrence is often a function of the level, so that they occur at a relatively strong levels of causing them tones. Another feature is the need for near-sinusoidal sounds of causing them tones.

Same conditions in other situations give rise to so-called. intermodulation distortion.

Still is debatable whether the combination tones occur in the air or are the result of complex processes in the ear. According to some studies, they can even arise in the brain.

Reasons for this are experiments in which one of them forming tones are transmitted only to one ear and the other – the other (using headphones). Part of the listeners were able to hear combinative tone in this situation.

This effect is called binaural beating.

## Standing Waves

When we have a superposition of two waves with the same frequency and amplitude, but moving in the opposite direction, we have a standing wave.

It manifests itself in the brass and string instruments as well as in space.

Therefore its effects are very important both in the distribution of waves in musical instruments, and in the sound field in which they travel.

In the rooms standing waves lead to strong non-linearity of the room, even when it is relatively well soundproofed.

This effect is observed primarily in the low frequencies.

At presence of opposing and parallel reflective surfaces in the room where the sound is emitted, a standing wave occurs between the main tone and its reflection on a frequency,  wich is a multiple of the distance between the surfaces as a wavelength. At this point, we have an increase of certain frequencies in specific areas of the room and a strong reduction in other areas.

Practically the room becomes highly nonlinear in the low frequencies and conditions are created for comb-filtering distortion in it.

This is the main reason the control room to be with non-parallel opposite walls, floor and ceiling. The separating window between the control room and the studio also is made by several pieces of glass, set at an angle in order to avoid this effect.

## Comb filtering

This effect occurs in two waves that are on certain spacing from each other and have the same or similar frequencies.

In contrast to large rooms where the delay effect between two wa
ves (eg primary and reflected) results in echo (when there are more than 18 meters distance between the walls), in small rooms we have a coloration of the sound caused by the filtration.

Short reflections with less than 20 ms delay create frequency nonlinearity in their interaction with the main signal. This leads to a practical impossibility for normal audition in such a room before you fix the problem by absorption and change the direction of walls and ceiling.

In such spaces, we can observe and other side effects besides comb filtering, such as ringing – effect and slap-back echo.

http://www.acs.psu.edu/drussell/Demos/superposition/superposition.html

http://www.physicsclassroom.com/class/waves/Lesson-3/Interference-of-Waves

https://en.wikipedia.org/wiki/Superposition_principle

End of this part

### Written byHristo

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