Sound waves approaching the ear enter either directly or are reflected by the pinnae down the meatus and are conducted to the cochlea by the three auditory ossicles (ie: the malleus, the incus and the stapes). The ossicular chain produces a pressure amplification of about 20:1. Their vibrations are conducted up the cochlea by the basilar fluid which excites about 30,000 small hair cells on the surface. It is from the motion of these hair cells that the brain interprets sound.

Cross section showing components of human ear.

The small pressure fluctuations we percieve as sound waves are imposed on a relatively stable atmospheric pressure. Given the way the ear is constructed, it is not sensitive to this constant pressure only the smaller fluctuations. (average atm = 101.325kPa). As an exercise using the the diagram above, try to determine just why the ear is not sensitive to atmospheric pressure (look at pressure equalisation via the Eustachian tube and the oval and round windows).

DIRECTION PERCEPTION

Interaural delay
Depends entirely upon time delays between similar excitement levels in each ear. The distance between each ear can be taken to be about 150mm. This means that there exists a vertical plane, running through the centre of the head, within which sound reach each ear simultaneously.

The Effects of the Pinnae
These are designed to collect frontal sound and reflect it down the aural canal. Sound entering from above and behind must have been diffracted by the pinea and, as a result, slight spectral changes to the sound will have occurred (more on diffraction later).

Subtle Head Movements
These assist in determining the height of a sound source in the medial plane (as described above).

DISTANCE PERCEPTION

The brain is also able to perceive the relative distance of a sound source as follows;

• Loss of intensity due to inverse square law and molecular absorption.

• Changes to the spectral content resulting from molecular absorption and diffraction around objects.

• The level of direct vs indirect sound - the age old trick of increasing reverberation as a song finishes in order to give the impression it is fading away into the distance, sounds like its in a large cave.

AUDIBLE RANGE

MEASURABLE CHARACTERISTICS

Power (Watts)
Measures energy output by a source, that sound's ability to do work.

Pressure (Pa)
Measures fluctuations about the local atmospheric pressure. Use of root-mean-square (rms) rather that peak-to-peak measures.

Intensity (W/m²)
The amount of sound energy within a specific area normal to the direction of propagation.

RESPONSE

Response = Measured Intensity / Threshold Intensity

Sound level measurements are generally referenced to a standard threshold of hearing at 1000 Hz for the human ear which can be stated in terms of sound intensity:

Iref = 10E-12 W/m²

or in terms of sound pressure:

Pref = 2E-5 Pa

Whilst these are the minimum thresholds, the table below details the range of audible sound. The upper limit actually represents the threshold of pain, where the sound it so loud it actually hurts the ear and may cause physical damage.

As you can see from the table, human pressure perception ranges from 20 micropascals up to 200 Pascal. This represents a considerable linear dynamic range (ie: 10E7). Because of this, and the way the ear works, it is convenient to firstly work with relative measurement scales rather than with absolute measurement scales, and secondly to logarithmically compress them.

DECIBELS

The units used to measure this ratio are called bels. Two variables differ by one bel if one is ten (1E1) times greater than the other, and by two bels if one is one hundred (1E2) times greater than the other. The bel is still a very large unit and it is more convenient to divide it into 10 parts - hence the decibel.

The standard threshold values given above corresponds to exactly 0 decibels. The actual average threshold of hearing at 1000 Hz is more like about 4 decibels, but zero decibels is a convenient reference.

LOUDNESS AND SOUND LEVELS

As opposed to a measurable characteristic, loudness is a subjective term describing the strength of the ear's perception of a sound. It is intimately related to sound intensity but can by no means be considered identical to intensity. The sound intensity must be factored by the ear's sensitivity to the particular frequencies contained in the sound. This is the kind of information contained in equal loudness curves for the human ear.

It must also be considered that the ear's response to increasing sound intensity is a "power of ten" or logarithmic relationship. This is one of the motivations for using the decibel scale to measure sound intensity. A general 'rule of thumb' for loudness is that the power must be increased by about a factor of ten to sound twice as loud.

Thus, a direct physical measurement of intensity, or even sound presssure, is almost meaningless in sensory terms unless it is referenced back to a threshold value. As the decibel is a relative measure and is used to quantify both pressure and intensity levels, each measurment can be compared to a universally accepted standard threshold value to derive a Sound Level in decibels (dB). Sound levels are directly meaningful in sensory terms.

Sound Power refers to the absolute power of a sound source (in Watts) whereas Sound Power Level (SWL) refers to the magnitude of that power relative to a reference power (in dB). Thus;

		W
SWL =	10 log(		)
		Wref

where Wref = 1E-12 W/m²

		I
SIL =	10 log(		)
		Iref

            where Iref = 1E-12 W/m²

		P²							P
SPL =	10 log(		)		or		SPL =	20 log(		)
		P²ref							Pref

where Pref = 2E-5 Pa

		(2E-5)²
SIL =	SPL + 10 log(		)
		(roc) * 1E-12

Obviously, given the density component (roc), the last term is pressure and temperature dependant. At 20'C and 1 atm it calculates out to around 0.1dB (Given that roc = 410 rayls). Thus:

SIL ~ SPL

Click here for some mathematical information on logarithms.

ACOUSTICAL POWER

The concept of acoustic power is not readily considered by most people, due in part to a preoccupation with sound pressure. To put it simply, sound pressure is the result of sound power. Sound power is the cause, sound pressure is the effect. The goal in loudspeaker design is to maximize the amount of acoustic power available from the device, given the constraints and trade-offs between the available parameters. Once the acoustic power has been realised, we then turn our focus to pattern control devices (horns) that will channel this power to a smaller unit area, increasing the sound intensity for that area, increasing the sound pressure (at a given listening position) beyond what it would have been if no pattern control was used.

In many conventional loudspeakers, it can take as much as 100 electrical watts to produce one acoustical watt, yielding an efficiency of about 1%. At the other extreme, a perfectly efficient transducer (that unfortunately does not and cannot exist) would produce one acoustic watt with the application of one electrical watt. Most cone-type transducers offer around 3% efficiency, with some advanced piezo-electric devices offering up to 20-25%.

One acoustic watt is equivalent to 107.5 dBSPL at around a meter from an omnidirectional source. A device's directivity can be described with a term called "Q", which is basically an indication of its ability to confine the applied energy to a smaller unit area. Q, therefore, is a parameter of the horn, not the driver. If we take one acoustic watt and couple it to a horn with a Q of 2 (hemispherical), the intensity and therefore the pressure will increase by a factor of 2 to 1 in the area covered by the device. This is quite useful, since it allows more energy on the audience and less on the walls and ceiling. It is common practice to convert the Q rating into decibels by the formula:

DI = 10 log(Q)

where DI is the directivity index.

The power of different sources of sound can vary widely. Different sources can also produce sounds with varying spectral content. A very shrill gas leak may produce the same sound power as a lawnmower, but they will be two very different sounds. Later, we will see how to take this into consideration when determining sound levels.

Sound Power Level of Typical Sources
From the IAC Noise Control Reference Handbook, 1989 Edition by Martin Hirschorn. © Copyright 1982, revised January 1989 by Industrial Acoustics Company

SOURCE	Sound Power, Watts	dB Re 10 -12  Watts
Saturn rocket	100,000,000	200
After burning jet engine	100,000	170
Centrifugal fan at 500,000 cfm (849,000 cu m/hr)	100	140
75 piece orchestra Vane axial fan at 100,000 cfm (169,900 cu m/hr)	10	130
Large chipping hammer	1	120
Blaring radio Centrifugal fan at 13,000 cfm (22,087 cu m/hr)	0.1	110
Auto on highway	0.01	100
Food blenders-upper range	0.001	90
Dishwashers-upper range	0.0001	80
Voice-conversational level	0.00001	70
Quiet-Duct silencer, self-noise at +1000 fpm	0.00000001	40
Voice-very soft whisper	0.000000001	30
Lowest audible sound for persons with excellent hearing	0.000000000001	0

REFERENCES

Nave C.R. 'Sensitivity of Human Ear' - Web Document
Department of Physics and Astronomy Georgia State University