Build a Sound System - 1A - Basic Audio Theory
Written by: dreamdustWritten on: Thu Sep 10, 2009 8:14 pm (This article has been viewed 682 times)
Article Description:
Basic Audio Theory:
This first section is going to be essentially theory, and will hopefully give you enough of a grounding to understand why we need to do the later practical stuff
Characteristics of an audio wave, and how it is perceived/interpreted by our hearing.
The conventional representation of an audio wave ie - all those very scientific pics that look like this:
are actually slightly misleading if you are trying to visualise the physical reality of one. It is correct in that it represents audio in the stated way, which is amplitude against time, and it is useful in many ways for analysis and editing, but it also leaves the impression that audio is a transverse wave (like a piece of string oscillating, or waves on a pond after a stone is dropped in). Audio is actually a longitudinal wave, and there are important differences in how they behave. So, though we will be using the above representation as a convenience in other parts of this document (it is called a wave graph), remember that it is only a useful convenience. Audiowaves are difficult to represent in 2 dimensions, as the physical reality is basically 4 dimensional - a set of pressure variations in 3 dimensions, emanating at a set speed from the source (which gives us the 4th dimension).
The major difference in behaviour between the two is the fact that longitudinal waves can propagate through gases and liquids, whereas transverse waves cannot (there is no mechanism for driving motion perpendicular to the propagation of the wave in transverse waves). For a full explanation of why and how, Hyperphysics has a good explanation here.
Because the waves are propagated outward from the source (assuming a point source - ie single point of radiation and no obstacles), audio waves obey the "inverse square law" of physics - basically, each time the distance from the source doubles, the sound pressure is quartered - represented by the equation P/4?r²=I (where P=source power, and I=Sound intensity). This gives an effective logarithmic drop off in the sound intensity as you move away from the source. Again, Hyperphysics has a good explanation of how this works (I will be referring regularly to the Hyperphysics website, and recommend it thoroughly as a source of scientific info generally) The inverse square law is obviously important to us in engineering audio amplification, as much of what we do will involve using other properties of audio waves to mitigate the inverse square characteristic.... I will go into this in more detail later on.
Our hearing mechanism essentially collects these pressure variations, and transmits them, via the tympanic membrane and the tiny bones (or Ossicles), into the inner ear, and Cochlea - which then converts the kinetic motion into electrical impulses to be transmitted to the brain... This is a very simplistic explanation for what is a quite complex set of interactions, and is explained in much more detail here. For our purposes, the other point to take note of along with the fact that our hearing apparatus is a very sensitive system is the action of the auditory canal (the bit that transmits sound from the outer ear onto the tympanic membrane). Because it acts essentially as a closed tube resonator, the auditory canal enhances sound in the range between 2 and 5KHz (which is, coincidentally, also the frequency range of the human voice). This rise in sensitivity is often referred to as the Fletcher/Munson curve (and is used extensively in perceptual compression techniques - ie MP3's etc). It also causes what is referred to as the bass loss problem - essentially, though all frequencies drop off according to the inverse square law, our hearing makes the drop off of bass frequencies much more pronounced (and means therefore that the bass frequencies need more reinforcement than those in the Fletcher/Munson curve)...
Methods of measuring audio levels.
As you will (hopefully) be aware from the above information, although audio follows measurable physical laws, there is also a lot that is down to subjective interpretation - the size and shape of the ear and auditory canal dictate where maximum sensitivity lies for a particular person (and because we are all different, there is a good deal of variation in these values). The efficiency of all parts of the ear in amplifying the pressure wave and transmitting it to the Cochlea creates variation in perception of overall loudness, and the efficiency of the Cochlea in converting kinetic energy into electrical creates yet more variation.... The question is - how do we create a set of measurements on which we can all agree, and which gives some objective basis of comparison for sound levels? This is an essential question if we hope to have any scientific basis from which to begin engineering our sound reinforcement. It has been answered in a number of ways - none of which are entirely satisfactory, but each of which arrives at some sort of consensus for use as an objective base.... They are:
1) Sound Pressure.
This is the most basic measurement, and also the most objective - it is a measurement of the sound pressure (obviously) at a given point and time in comparison to atmospheric pressure, stated in newtons/m². It is of relatively limited use, because although it is a direct measurement of the pressure wave, it is a limited snapshot at a given time - to be useful we need a measurement of these snapshots over time, or an average level.
2) Sound Intensity.
This is the sound power per unit area, the usual context being a measurement of the average intensity at a given point. It is measured in Watts/m², or acoustic watts. Unlike the sound pressure measurement, this is a measurement of the sound energy at a given point as an average over time.
From this point, we need to relate the subjective sensation of loudness to some objective base. The way this is achieved is by the use of the Decibel scale or dB (named after Alexander Graham Bell - it equals 1/10th of a Bell). The basic premise is - when a sound of intensity I falls on the ear, what change ?I will cause the hearer to report a barely audible change in the sensation of loudness. Our hearing turns out to be so constructed that ?I is proportional to I - that is the more intense the sound, the greater ?I must be. So:
3) The Decibel scale, or dB.
Is a logarithmic scale used to measure loudness relative to a baseline known as the threshold of hearing. The threshold of hearing is an intensity of 10?¹²W/m² - chosen because it is near the lower limit of human audibility. The expression of loudness is then obtained by I(dB)=10log(¹º)[I/Iº], where I=the intensity, and Iº=the threshold of hearing. For an in depth analysis of this calculation, and how it is used, see this page. This scale is a useful measure of loudness, and is the standard measurement used in audio. It is not perfect however, as the human ear's perception of loudness changes based on frequency (due to the effect of the auditory canal). The dB scale can be altered by use of contour filters (which effectively filter out frequencies that the ear does not hear well in order to more effectively simulate human hearing). Most common of these is the:
4) dBA - dB of sound with an "A" contour filter.
This the most commonly used contour filter, as it most closely mimics the hearing curve of the human ear. See here for a description of how it works - it is the scale generally used to measure the loudness at venues etc, or to measure ambient sound on a site etc.
These are the basic and most common measurements; there are others, either using different contour filters, or more closely relating the loudness by plotting equal loudness curves for the human ear, and then relating a dB value at a set frequency as in the Phon and Sone scales.
5) SPL, or Sound Pressure Level.
This is a measurement commonly used in the specs for speaker drivers, as one axis of a frequency response graph. Basically, the SPL is measured in dB when the speaker or system is fed 1Watt of electrical power, by placing a microphone 1m away - hence the curves shown on driver specs which show the output at varying frequency in dB SPL at 1w/1m. It is useful as a rough guide only, and shouldn't be used as a guide to speaker driver quality (if you check such ratings, you will notice that mid range and tweeters invariably have higher dB ratings than woofers).
So, that is the basic physics/biology of audio - obviously there is a lot more, but hopefully this information should give you a sound basis. Again, I can recommend to you the Hyperphysics site which contains a huge amount of the theoretical information on sound, along with many of the engineering practices generally used.
For our purposes, and in conclusion we can reiterate the points that are going to be of most use to us in building our rig:
Audio is transmitted through air as a longitudinal wave, and follows the Inverse square law of physics. This logarithmic drop off in sound intensity is what we need to engineer to compensate for.
Our perception mechanism for sound is most sensitive in the human vocal range of 2-5KHz, and shows a marked drop off at the bass frequency range - we therefore need to reinforce these frequencies to compensate.
There are many ways of measuring audio, none of which are entirely satisfactory. The ones we will mostly be using however are: Intensity, measured in Acoustic watts (W/m²). Loudness, measured in dB, and ambient loudness measured using a contour filter (in dBA).
In the next section, we will investigate how audio is created or manipulated for the purpose of amplification.
This first section is going to be essentially theory, and will hopefully give you enough of a grounding to understand why we need to do the later practical stuff
Characteristics of an audio wave, and how it is perceived/interpreted by our hearing.
The conventional representation of an audio wave ie - all those very scientific pics that look like this:
are actually slightly misleading if you are trying to visualise the physical reality of one. It is correct in that it represents audio in the stated way, which is amplitude against time, and it is useful in many ways for analysis and editing, but it also leaves the impression that audio is a transverse wave (like a piece of string oscillating, or waves on a pond after a stone is dropped in). Audio is actually a longitudinal wave, and there are important differences in how they behave. So, though we will be using the above representation as a convenience in other parts of this document (it is called a wave graph), remember that it is only a useful convenience. Audiowaves are difficult to represent in 2 dimensions, as the physical reality is basically 4 dimensional - a set of pressure variations in 3 dimensions, emanating at a set speed from the source (which gives us the 4th dimension).
The major difference in behaviour between the two is the fact that longitudinal waves can propagate through gases and liquids, whereas transverse waves cannot (there is no mechanism for driving motion perpendicular to the propagation of the wave in transverse waves). For a full explanation of why and how, Hyperphysics has a good explanation here.
Because the waves are propagated outward from the source (assuming a point source - ie single point of radiation and no obstacles), audio waves obey the "inverse square law" of physics - basically, each time the distance from the source doubles, the sound pressure is quartered - represented by the equation P/4?r²=I (where P=source power, and I=Sound intensity). This gives an effective logarithmic drop off in the sound intensity as you move away from the source. Again, Hyperphysics has a good explanation of how this works (I will be referring regularly to the Hyperphysics website, and recommend it thoroughly as a source of scientific info generally) The inverse square law is obviously important to us in engineering audio amplification, as much of what we do will involve using other properties of audio waves to mitigate the inverse square characteristic.... I will go into this in more detail later on.
Our hearing mechanism essentially collects these pressure variations, and transmits them, via the tympanic membrane and the tiny bones (or Ossicles), into the inner ear, and Cochlea - which then converts the kinetic motion into electrical impulses to be transmitted to the brain... This is a very simplistic explanation for what is a quite complex set of interactions, and is explained in much more detail here. For our purposes, the other point to take note of along with the fact that our hearing apparatus is a very sensitive system is the action of the auditory canal (the bit that transmits sound from the outer ear onto the tympanic membrane). Because it acts essentially as a closed tube resonator, the auditory canal enhances sound in the range between 2 and 5KHz (which is, coincidentally, also the frequency range of the human voice). This rise in sensitivity is often referred to as the Fletcher/Munson curve (and is used extensively in perceptual compression techniques - ie MP3's etc). It also causes what is referred to as the bass loss problem - essentially, though all frequencies drop off according to the inverse square law, our hearing makes the drop off of bass frequencies much more pronounced (and means therefore that the bass frequencies need more reinforcement than those in the Fletcher/Munson curve)...
Methods of measuring audio levels.
As you will (hopefully) be aware from the above information, although audio follows measurable physical laws, there is also a lot that is down to subjective interpretation - the size and shape of the ear and auditory canal dictate where maximum sensitivity lies for a particular person (and because we are all different, there is a good deal of variation in these values). The efficiency of all parts of the ear in amplifying the pressure wave and transmitting it to the Cochlea creates variation in perception of overall loudness, and the efficiency of the Cochlea in converting kinetic energy into electrical creates yet more variation.... The question is - how do we create a set of measurements on which we can all agree, and which gives some objective basis of comparison for sound levels? This is an essential question if we hope to have any scientific basis from which to begin engineering our sound reinforcement. It has been answered in a number of ways - none of which are entirely satisfactory, but each of which arrives at some sort of consensus for use as an objective base.... They are:
1) Sound Pressure.
This is the most basic measurement, and also the most objective - it is a measurement of the sound pressure (obviously) at a given point and time in comparison to atmospheric pressure, stated in newtons/m². It is of relatively limited use, because although it is a direct measurement of the pressure wave, it is a limited snapshot at a given time - to be useful we need a measurement of these snapshots over time, or an average level.
2) Sound Intensity.
This is the sound power per unit area, the usual context being a measurement of the average intensity at a given point. It is measured in Watts/m², or acoustic watts. Unlike the sound pressure measurement, this is a measurement of the sound energy at a given point as an average over time.
From this point, we need to relate the subjective sensation of loudness to some objective base. The way this is achieved is by the use of the Decibel scale or dB (named after Alexander Graham Bell - it equals 1/10th of a Bell). The basic premise is - when a sound of intensity I falls on the ear, what change ?I will cause the hearer to report a barely audible change in the sensation of loudness. Our hearing turns out to be so constructed that ?I is proportional to I - that is the more intense the sound, the greater ?I must be. So:
3) The Decibel scale, or dB.
Is a logarithmic scale used to measure loudness relative to a baseline known as the threshold of hearing. The threshold of hearing is an intensity of 10?¹²W/m² - chosen because it is near the lower limit of human audibility. The expression of loudness is then obtained by I(dB)=10log(¹º)[I/Iº], where I=the intensity, and Iº=the threshold of hearing. For an in depth analysis of this calculation, and how it is used, see this page. This scale is a useful measure of loudness, and is the standard measurement used in audio. It is not perfect however, as the human ear's perception of loudness changes based on frequency (due to the effect of the auditory canal). The dB scale can be altered by use of contour filters (which effectively filter out frequencies that the ear does not hear well in order to more effectively simulate human hearing). Most common of these is the:
4) dBA - dB of sound with an "A" contour filter.
This the most commonly used contour filter, as it most closely mimics the hearing curve of the human ear. See here for a description of how it works - it is the scale generally used to measure the loudness at venues etc, or to measure ambient sound on a site etc.
These are the basic and most common measurements; there are others, either using different contour filters, or more closely relating the loudness by plotting equal loudness curves for the human ear, and then relating a dB value at a set frequency as in the Phon and Sone scales.
5) SPL, or Sound Pressure Level.
This is a measurement commonly used in the specs for speaker drivers, as one axis of a frequency response graph. Basically, the SPL is measured in dB when the speaker or system is fed 1Watt of electrical power, by placing a microphone 1m away - hence the curves shown on driver specs which show the output at varying frequency in dB SPL at 1w/1m. It is useful as a rough guide only, and shouldn't be used as a guide to speaker driver quality (if you check such ratings, you will notice that mid range and tweeters invariably have higher dB ratings than woofers).
So, that is the basic physics/biology of audio - obviously there is a lot more, but hopefully this information should give you a sound basis. Again, I can recommend to you the Hyperphysics site which contains a huge amount of the theoretical information on sound, along with many of the engineering practices generally used.
For our purposes, and in conclusion we can reiterate the points that are going to be of most use to us in building our rig:
Audio is transmitted through air as a longitudinal wave, and follows the Inverse square law of physics. This logarithmic drop off in sound intensity is what we need to engineer to compensate for.
Our perception mechanism for sound is most sensitive in the human vocal range of 2-5KHz, and shows a marked drop off at the bass frequency range - we therefore need to reinforce these frequencies to compensate.
There are many ways of measuring audio, none of which are entirely satisfactory. The ones we will mostly be using however are: Intensity, measured in Acoustic watts (W/m²). Loudness, measured in dB, and ambient loudness measured using a contour filter (in dBA).
In the next section, we will investigate how audio is created or manipulated for the purpose of amplification.
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