HEARING
Pressure Waves = layers of high or low pressure propagate in a similar fashion as a perturbation in a chain
of marbles connected by springs.
Pressure is measured at a particular point in space varies over time as the layers of high and low pressure
pass across the point of measurement.
Amplitude = pressure at the peaks of the pressure waveform.
Intensity = “sound energy passing through a unit area per unit time. Unit = Watts per m² (W/m²)
The intensity of a sound (l) is proportional to the square of its pressure (P) l = K-P²
Dynamic Range (range of hearing)
The faintest sound we can hear has a pressure of ~20 µPa
Humans can process sounds with a pressure of ~20,000,000 µPa before feeling pain.
In terms of pressure the hearing range corresponds to a factor of 1 million, and in intensity terms, 1
trillion, or 1 million millions.
Thus, using ordinary pressure or intensity units would mean having to deal with huge and unwieldy
numbers.
Instead pressure and intensity are specified in logarithmic units called decibels sound pressure level (dB
SPL)
L dB SPL= 20 log10 (P/20µPa)
Faintest Audible sound (20µPa) = 0 dB SPL
Pain Threshold (20,000,000 µPa) = 120 dB SPL
Frequency Decomposition
Simplest possible sounds = pure tones – with a sinusoidal pressure waveform
Waveforms repeat themselves over time (temporally periodic); rate of repetition = frequency.
Frequency is measured in repetitions (cycles) per second or Hertz (Hz)
1 repetition/s = 1 Hz; 1000 repetitions = 1000 Hz = 1 kHz.
In order to characterize a pure tone, one needs to specify: Frequency, Amplitude, Starting phase.
Starting phase = describes any temporal offset in the pure tone’s pressure waveform.
Mathematically, the waveform of a pure tone is give by the equation p(time) =Asin2πF-time-starting
phase. (The sine function, multiplied by the amplitude, A; the sine function has two arguments, one that
depends on the frequency, F, and the starting phase.
Most sounds encountered in realistic environments look very different from tones.
Surprisingly, these widely differing waveforms – and, indeed, any waveform – can be produced by adding
together pure tones of different amplitudes, frequencies and phases.
Pure tones are the basic building blocks of sounds; the whole concept of frequency is based on sinusoids.
Just as it is possible to build up a sound, it is also possible break down into a set of pure tones.
Sounds can be unambiguously described in terms of their sinusoidal frequency components.
In analogy to the spectrum of light as analyzed through a prism, the description of sound in terms of its
frequency components is referred to as a spectrum; the mathematical technique used to compute it is the
Fourier Analysis.
The spectrum shows the levels of the sound’s sinusoidal components as a function of frequency.
, STRUCTURE OF THE EAR
Outer Ear
The outer ear consists of the auricle and the ear canal
The outer ear “filters” the incoming sound – lets some frequencies through better than others
The frequency transfer characteristics of the outer ear depend on the direction which the sound is coming
from.
Middle Ear
The outer ear is separated from the middle ear by the eardrum (tympanic membrane) which is pushed
inwards and outwards by the sound waves.
The middle ear is connected to the back of the throat by the Eustachian (auditory) tube, which can be
opened by yawning or swallowing – this balances the pressure inside the middle ear with outside the ear
Ossicles – the eardrum is connected to the inner ear by three tiny bones- the auditory ossicles.
The ossicles amplify the pressure of the eardrum’s vibrations like a lever and transmit them through the
membrane of the oval window into the fluid filled cavity within the bony shell of the cochlea in the inner
ear.
Inner Ear
Cochlea – thin, fluid filled tube (3.5cm long), curled up like a snail
It’s divided into two components – the scala vestibule and the scala tympani, separated by the basilar
membrane.
When the oval window moves inwards or outwards (due to the vibration of the ossicles) causes a
pressure difference between scala vestibule and the scala tympani the basalir membrane is pushed
downwards or pulled upwards similar to a water wave, this perpetration propagates from the base to
the tip (apex) of the cochlea.
This pattern of vibration is called the travelling wave
Travelling Wave
The mechanical properties of the basalir membrane change along its length; the membrane is narrow and
stiff and its basal end and becomes progressively wider and more floppy towards the apex.
Due to this mechanical gradient, the amplitude of the travelling wave changes as the wave progresses
along the membrane, increasing till its reaches its maximum at a point of resonance, beyond which the
wave then dies very abruptly.
Importantly, the point at which resonance is reached, depends on the frequency of the sound, because
the narrow and stiff basal end of the basilar membrane responds better to high frequencies, whereas the
wide and floppy apical end responds better to low frequencies
Different frequencies stimulate the basilar membrane at different points along its length, high frequencies
at the base, medium frequencies in the middle and low frequencies at the apex.
This means that the cochlea acts as a frequency anaylser, decomposing sounds into their component
frequencies and creating a topographic map of frequency along the length of the basilar membrane.
Referred to as the tonotopic map.
Organ of Corti – Auditory receptor organ
The mechanical response of the basilar membrane is converted into electrical brain activity by the organ
of corti.
