Acoustics & Signal Processing

To understand how the brain can learn so much from the sounds in our environment, we must first understand why objects and events around us create sounds in the first place. Physical acoustics studies the creation and propagation of sound waves. Fundamental concepts of physical acoustics are discussed in chapter 1 of "Auditory Neuroscience" . This collection of web pages further illustrates ideas related to sound generation, sound propagation, and the physical description and manipulation of sounds.

Simple Harmonic Motion - Animation

Many objects in nature can be thought of as "mass-spring-systems" because they are composed of objects which have inertial mass as well as a spring like stiffness. It is natural for mass spring systems to enter into sinusoidal oscillation. These oscillations may create vibrations of the surrounding air (i.e. periodic sounds), as described under "sound propagation" below.
This figure is an animated version of Figure 1-1 of "Auditory Neuroscience"

The thing to take away from this are the following:

Mystery Object A:

Mystery Object B:

Modes of Vibration - Animation

A guitar string, plucked at the centre, will be stretched into a triangular shape before you let it go. Once you let it go it will vibrate in a "triangular sort of way". The thing about its motion is that it can be thought of as a superposition of simple harmonic motions, with harmonically related frequencies, as shown here. The "more or less triangular" vibration in the lowest panel arises as a weighted sum of the three modes of vibration shown above it. 

This animation complements Figure 1-3 of "Auditory Neuroscience"

Modes of vibration of a 2-D plate - youtube video

In this youtube video, a black, square plate is made to vibrate sinusoidally at a given, gradually increasing frequency. A white powder, sprinkled onto the plate, will come to rest only at the nodes of the predominant mode of vibration of the plate, which renders the nodes visible as white lines. As the frequency increases, it excites modes of vibration of ever higher order, making intricate patterns consisting of increasingly larger numbers of lines.  Note that here the plate is excited with a sinusoidal vibration, so it will exhibit only one mode of vibration at a time, the one that corresponds to the overtone closest to the input frequency. If the plate was instead struck, it would vibrate at all these modes at once, making a rich, metallic "clink" sound with lots of overtones.


Modes of Vibration Caught on Camera

In the previous animation you have seen how a plucked guitar string will vibrate at numerous "modes of vibrarion" at once, and therefore produce sound at many harmonically related frequencies ("overtones"). Just to show that these modes of vibration are real, here a little youtube video by nicogetz, where he placed a camera phone inside his guitar and then played a tune. The camera phone is too slow to pick out all the details of the motion of the strings (the phone will collect somewhere around 40 to 70 frames a second, while the highest harmonics of the motion of the strings may vibrate at several thousand frames a second) but the result is that only some of the modes of vibration will be "aliased" by the video to become visible to the naked eye. Nevertheless a beautiful illustration to show that modes of vibration are a feature of sound sources.


This javascript app calculates a spectrogram from the input to your computer's microphone. (You may have to adjust the sensitivity a bit.) A spectrogram is in some ways similar to the activity pattern that auditory nerve fibers send to your brain, so you can use this spectrogram app to visualize what various sounds or speech would "look like" to your brain. You can pause the spectrogram by clicking on it.

Realtime Spectrogram - Freeware program

Spectrograms can be useful to visualize the frequency content of sounds, and to give a rough-and-ready approximation of the activation pattern a sound is likely to generate across the auditory nerve array. For classroom demonstrations, or just to explore sounds, it's nice to have a piece of software which will record sounds from the microphone of your computer and will display the spectrogram online on the computer screen. One nice freeware program for that purpose was created by a company called Visualization Software, but their website seems to have gone off air (perhaps the company ceased to exist). This screenshot shows the program in action, visualizing the spectrogram of me pronouncing the vowels /a/-/e/-/a/-/e/-/a/ . The change in formants as well as the harmonic of the vowels are showing up clearly. spectrogram screenshot As it is a very nice and useful little freeware program I am making the installation file available here. It's a Window's program. It comes with absolutely no warranties! My virus checker thinks it's kosher, and when I've used it for lectures and classroom use it has always performed beautifully (kudos to the folks from Visualization Software!), but use it at your own risk. (And since I am not the author, please don't send me any bug reports - I would not know what to do with them).

Sound Propagation - Animation


Sound propagates as a longitudinal wave. Although air is relatively light, it does weigh something. Air is also "elastic": if you try to compress it, it will push back. Given that air has both elasticity and mass, you can imagine the air around you as being made up of little "lumps of air", where each lump is connected to the next lump by an elastic spring.

If an object (e.g. the small bar at the left edge of the animation below) pushes against such a column of air, it compresses the air immediately next to it. This compression propagates away from the object as a "compression wave", as each lump of air pushes against its next neighbor. If the object then returns to its original position, it draws the air back, creating a "rarefaction wave" which follows the compression wave.

The animation here, essentially an animated version of Figure 1.17 of "Auditory Neuroscience", illustrates this.

The Inverse Square Law

In the "free field" (meaning in the absence of obstacles that might interfere with wave propagation), sound waves will spread out in all directions, like spheres radiating out from the source at the speed of sound.

Clearly, as the radius of the spheres gets larger, the amount of acoustic energy in the sound gets "stretched thinner and thinner" over the expanding surface of the sphere. Given that the surface of a sphere is proportional to the square of its radius (A = 4⋅π⋅r2), the energy in the sound wave that would impinge on a fixed small area (e.g. an ear drum) therefore declines with the square of the distance from the source.

This relationship between sound intensity and distance from the source is known as the inverse square law.

Note that in closed rooms where considerable amounts of sound energy may be reflected back from walls, floor or ceiling, the inverse square law usually does not hold.

Clinical Audiograms and Hearing Level (dB HL)

Clinicians measure sound intensity in dB HL (decibels Hearing Level), i.e. dB relative to the quietest sounds that a young healthy individual ought to be able to hear.  In a clinical audiogram test, pure tones between ca 250 and 8000 Hz are presented at varying levels, to determine a patient's pure tone detection thresholds (the quietest audible sounds) in the left and right ear. Thresholds between -10 and +20 dB HL are considered in the normal range, while thresholds above 20 dB HL are considered diagnostic for mild, moderate, severe or profound hearing loss, as shown here:

clinical audiogram levels


Particular causes of hearing loss will be show up in the clinical audiogram in characteristic ways.

Conductive Hearing Loss 

Conductive hearing loss comes about when the transmission of sound to the inner ear is impaired, perhaps due to impacted ear wax (cerum), an ear infection (otitis media with effusion or OME), or calcification of the middle ear ossicles (otosclerosis). Conductive hearing loss tends to a loss of sensitivity across the entire range of frequencies, most commonly in one ear only. A so called "bone conduction test", where sound is delivered as vibration to the skull rather than as airborne sound to the ear canal, can be used to confirm a suspected conductive hearing loss. 

conductive hearing loss audiogram


(image source: US Occupational Health Administration)

It is often possible to treat conductive hearing loss by removing the cause of the physical obstruction.


Sensory-Neural Hearing Loss

By far the most common cause of sensory neural hearing loss is damage to sensory hair cells in the cochlea. The outer hair cells in particular are very fragile, and can be damaged by exposure to excessively loud sounds, or they may simply "wear out" in old age. In rarer cases, hair cells can also be damaged by certain chemicals (such as high doses of aminoglycoside antibiotics).  Sensory-neural hearing loss can also be caused by damage the auditory nerve, but conditions producing such damage are relatively rare, while noise damage or age related hearing loss are very common complaints. Central hearing loss (due to damage to the central nervous system) is rarer still. Noise damage or age related hearing loss tends to produce characteristic deficits as shown in the audiograms here below. Unlike conductive hearing loss, which can often be cured, sensory-neural hearing loss is in most cases irreparable, and treatment will aim to make the best use of those auditory structures that remain in tact, perhaps by boosting sensitivity through a hearing aid, or, in severe cases, by trying to bypass dead sensory hair cells with cochlear or brainstem implants.


Noise damage

Because our outer and middle ear transmits frequencies near 4 kHz very efficiently, hair cells that are tuned to frequencies near 4 kHz are particularly vulnerable to noise damage. Therefore, audiograms of patients with noise damage often have characteristic 4 kHz notches, as shown here:

Clinical audiogram showing typical noise damage


(image source: Simon Fraser University, Canada)


Age-related Hearing Loss (Presbycusis)

Even if we avoid exposure to very loud noise, the ear's outer hair cells may also simply wear out as we age, leading to age related hearing loss. In this condition, high frequency outer hair cells tend to die off before low-frequency ones, possibly because the high frequency outer hair cells have to work harder if their job is to amplify acoustic vibrations on a cycle by cycle basis. Consequently, patients with age-related hearing loss often have normal sensitivity at low frequencies, but progressively poorer sensitivity for higher frequencies, as shown here:

average hearing loss graph

If you are curious about what the effect of such age related hearing loss would be, try our Age Related Hearing Loss Simulator)