Sound and Hearing

Sound travels as Longitudinal waves The oscillations are parallel to the direction of energy transfer. Direction of energy transfer oscillation

Longitudinal waves compression rarefaction

The Ear

The Ear

Outer Ear The sound is reflected by the sides and channeled into the auditory canal.

There is a pressure difference between the two sides of the ear drum (the inside pressure is kept constant due to the Eustachian tube connecting with the back of the nose) Force on left = (P + ΔP)A Force on right = PA Unbalanced force = ΔPA This force is very small and needs to be amplified to move the liquid in the cochlea Ear Drum P + ΔP Area A P

The Middle Ear - Ossicles The small bones (ossicles) are arranged to pass on the vibration arranged as levers to amplify the FORCE (but small movement)

The Middle Ear - Ossicles F1 F2 d2 d1 L1 L2 Work done by F1 = F1d1 Work done by F2 = F2d2 so by conservation of energy F1/F2 = d2/d1, and since d2<d1, F2>F1 Amplification factor = d1/d2 = L1/L2

The Middle Ear - Ossicles The small bones (ossicles) also help to dampen the vibrations of the ear drum.

The Middle Ear – Ossicles Sound travelling from air to liquid is normally reflected (99.5%). The amplification by the ossicles raises the amount of sound transferred to 50%.

The Middle Ear – Cochlea window A given force will result in a higher pressure as the area of the oval cochlea window is small compared to the ear drum.

The Middle Ear – Cochlea window F = ΔP1A1 ΔP2 = ΔP1A1 /A2 ΔP1 Since A2<A2 the pressure difference is amplified, amplification factor = A1/A2

The Inner Ear - Cochlea This is a 2cm long coiled tube containing a liquid. The vibrating oval window causes the fluid to be pushed along the tube (causing another round window to bulge outwards) which disturbs small hairs on the wall of the cochlea. These sends messages along the auditory nerve to the brain.

Intensity of a Wave Remember from topic 4 that the intensity of a wave is the amount of energy passing through a unit area per unit time. It is normally measured in W.m-2.

Intensity at a distance from a light source I = P/4πd2 where d is the distance from the light source (in m) and P is the power of the light source(in W)

Intensity at a distance from a light source I = P/4πd2 d

Sound Intensity Level The sound intensity level attempts to quantify the sensation of hearing. It relates sounds to the lowest intensity that can normally be heard by a human ear (1 x 10-12 W.m-2) Sound intensity level (dB) = 10log(I/Io) where Io = 1 x 10-12 W.m-2.

Note! Note the important difference between sound intensity (measured in W.m-2) and sound intensity level (measured in dB) SIL (dB) = 10log(I/Io)

Example “Physics for the IB Diploma”, K.A. Tsokos, CUP The intensity of a sound increases from 10-10 Wm-2 to 10-8 Wm-2. By how much does the sound intensity level change?

Example “Physics for the IB Diploma”, K.A. Tsokos, CUP The intensity of a sound increases from 10-10 Wm-2 to 10-8 Wm-2. By how much does the sound intensity level change? Original level = 10log(10-10/10-12) = 10log102 = 20 dB New level = 10log(10-8/10-12) = 10log104 = 40dB Increase is thus 20 dB

The decibel scale dB

A vacuum cleaner A vacuum cleaner has a SIL of 80 dB. What is its intensity? 80 dB = 10log(I/Io) 8 = log(I/Io) 108 = I/Io = I/(1 x 10-12) I = 1 x 10-4 W.m-2

Let’s try some questions!

Hearing Defects

Sensory nerve deafness Damage to the cochlea and/or neural pathways (nerves) Possibly due to tumours of the acoustic nerve or meningitis. Acoustic trauma (injury caused by loud noise) can damage hair cells.

Conductive deafness Damage to the middle ear prevents transmission of sound to the cochlea Destruction or seizing of the ossicles due to serious infection or head injury (Otosclerosis - an abnormal growth of bone in the middle ear). Ear could be blocked by wax or an obstruction Eardrum could have thickened due to repeated infections/rupture

Hearing tests http://www.wisc-online.com/Objects/ViewObject.aspx?ID=MBY1802

Hearing tests Normally sounds of 125, 250, 500, 1000, 4000, 8000 Hz are played through headphones. Sounds start very quietly and increase until the patient can hear them. Made for both ears AND with a vibrator attached to the bone behind the ear to send sound directly to the cochlea through the bone.

Audiogram The hearing level in dB is then plotted against frequency to produce an audiogram.

Audiogram Hearing can be tested using an audiogram Bone conduction Air conduction

Conductive loss You can see that the hearing through the bone (straight to the cochlea) is fine, but the hearing through air is not. This indicates conductive hearing loss (cochlea is working fine). A hearing aid may help

Typically exposure to loud noise over time will see a dip at 4000 Hz. Sensory Loss You can see here that the lines for air conduction and bone conduction follow each other (and lower). This is a sure sign of sensory loss. A cochlea implant may be useful.

Ageing Aging produces a more gentle downward curve. This is the natural decline in hearing that many people experience as they get older. It's partly due to the loss of hair cells in the cochlea.

Clear? http://www.lloydhearingaid.com/shopping/audiogram_start.asp