Before we start to grapple with psychoacoustics, it is useful to know a little about how human hearing works. Figure 1 shows a diagram of the main components. Sound waves from the outside world enter through the external part of the ear, into the auditory canal. This is an acoustic duct, which functions rather like an ear trumpet to concentrate the energy of the sound wave before it reaches the tympanic membrane, or eardrum. The sound level at the eardrum is boosted by up to 15 dB compared to the incident sound wave, peaking around 3 kHz. The eardrum is a membrane that is set into vibration by the incoming sound wave. The next part of the system is the middle ear, containing three tiny bones (the malleus, incus and stapes) which act as a kind of lever system to increase the force available from the vibration.
Now we enter the most important region, the inner ear. The complicated shape drawn in purple indicates a cavity within the bone of your skull. It has two main components. The semi-circular canals are associated with our sense of orientation and balance: it has components which behave rather like the accelerometers and gyros that you may have inside your mobile phone, to sense accelerations and rotational movement.
The component we are most interested in is the second one, the cochlea. It is wound up into a shape like a snail shell: indeed, the word “cochlea” derives from the Greek for a snail. The cochlea is a bony cavity, and it is filled with fluid. It has two “windows”: flexible membranes that hold the fluid in, but able to bulge in and out . The final bone of the chain in the middle ear, the stapes, presses against one of these windows, the oval window, and it pushes it in and out as a result of the incoming sound wave. The fluid inside the cochlea is virtually incompressible, so to accommodate this movement there is a second window, the round window, which can bulge in the opposite sense to the oval window.
To see the point of this, we need to know a bit about what is inside the cochlea. Figure 2 shows an “unrolled” view of it. Glossing over a lot of complicated anatomical details (see Wikipedia if you want to know more), the crucial component for our purpose is called the basilar membrane. This membrane bridges across the cochlea from side to side. The oval window introduces acoustic disturbances on one side of it, while the round window allows them to “escape” on the other side. The resulting fluid flow in the cavity exerts a force across the basilar membrane, making it vibrate.
Now for the important part: the mechanical properties of the basilar membrane vary, by an enormous factor, along the length of the cochlea. At the end near the two windows, it is narrow and stiff, while at the far end it is wider and floppier. The result is that the basilar membrane functions as a kind of mechanical frequency analyser. If the incoming sound wave is sinusoidal, the vibration response of the basilar membrane is concentrated in a particular region: near the base for a high frequency, near the far end for a low frequency. Some positions of maximum response for different frequencies are indicated in Fig. 2 (but note that more recent research suggests that the lowest indicated frequency may be a bit misleading: the peak frequency at the end of the cochlea may be 50 Hz).
The basilar membrane carries a large number of hair cells, which are the neural sensors for vibration. So, at least to an extent, the information reaching the brain along the auditory nerve is already sorted out into its frequency content, simply because nerve fibres originating from hair cells attached at different positions on the basilar membrane will tend to respond most strongly to sounds in different frequency ranges, appropriate to the position of each one. We will see in section 6.4 that some aspects of this mechanical filtering action of the basilar membrane carry over rather directly into the way we hear.
When you listen to sound that is sufficiently quiet, this mechanical response of eardrum, middle ear and basilar membrane involves small-amplitude vibration, and can be described reasonably well by the kind of linear theory we have been using up to now. But the sound does not need to become very loud before the response starts to exhibit progressive nonlinearity. In any case, from here on the process of hearing is very definitely nonlinear. The nervous system communicates in the form of electrical pulses, so the brain is essentially a digital device. The information from individual hair cells is coded, somehow, in the rate and detailed timing of the pulses generated and sent off along the auditory nerve by the neurons connected to them.
However, this is not the end of mechanical effects that influence hearing. Not all the hair cells are sensors. Some of them, indeed the majority of them, behave like loudspeakers: they cause additional motion of the basilar membrane in response to nerve signals coming back from the brain or from a more local reflex action. These active hair cells are known as outer hair cells, whereas the sensing hair cells are inner hair cells. Sometimes, the action of the outer hair cells results in sound coming out of the ears: so-called otoacoustic emissions. Some kinds of tinnitus are the result of real sounds generated in the ear in this way. The details of the excitation of the basilar membrane by these active hair cells are still a matter of current research, but it appears that this process is crucial to the phenomenal range of loudness that our ears are capable to responding to. We will say more about that in the next section.
For more detail of all aspects of cochlear mechanics, see the comprehensive review by Ni et al. .
 Guangjian Ni, Stephen J. Elliott, Mohammad Ayat, and Paul D. Teal: “Modelling cochlear mechanics”, BioMed Research International, Volume 2014, Article ID 150637, 42 pages http://dx.doi.org/10.1155/2014/150637