illiifi:lT The of

Learning outcomes

On completion of this section, youshoutd be able to:

r explain how the ear responds toan incoming sound wave

r understand the significanceof the terms sensitivity and

f req uency response

r state the magnitude of thethreshotd of hearing

r state the intensity at whichd iscomfort is experienced

r use the equation for intensityIeveI

r understand the terms nolse arrd

loudness.

anvil

a u d itorynerve

tympanicrnembrane ;eustachian tube

The human earFigure I2.L.1, shows a dtagram of the human ear.

The outer ear collects and directs sound waves into the auditory carral. Atthe end of the auditory canal is the tympanic membrane (ear dmm). Thesound waves cause the tympanic membrane to vibrate. The middle earconsists of three tiny bones called the hammeq the anvil and the stirrup.When the tympanic membrane vibrates, the bones in the middle earvibrate as well. The three bones act like a lever system. They reduce theamplitude of vibration produced on the tympanic membrane. At the sametime, the vibrational pressure on the oval window is increased.

The middle ear is connected to back of the throat via the eustachiantube. Under normal conditions, the pressure on both sides of thetympanic membrane is the sanle. When someone ascends in an aucraft,pressure difference exists on either side of the tympanic mernbrarteresulting in the ear " popping".

The inner ear is filled with liquid. It contains the cochlea, which isattached to auditory nerve. Inside the cochlea there ate :rrrany tiny hairsthat run its entire length. These hairs .vary in length, thickness andstiffness. When the oval window vibrates, the liquid inside the inner earvibrates causing the tiny hairs to resonate. The hairs produce electrtcalsignals which are then transmitted via the auditory nerve to the brarn,where they are then interpreted.

Frequency response and intensityThe human ear is able to detect frequencies in the range 20Hz to 20L<812.

This range is called the frequency response of the ear. As a person gets oldeqthe upper limit of 20kHz decreases. In the frequency range 60Hz to 1 l<I12,

the human ear can detect changes of ZHz to 3 Hz. At frequencies abovell<L{2, it is difficult for the human ear to detect r*?]1 changes in frequencies"

Intensity is the sound power per unit ^re^ lII

: Aj *astatedfrequency'

The smallest sound intensity that can be detected by the human ear is calledthe threshold of hearing. The threshold of hearing is 1.0 x 10-12Wm-2 at afrequency of 3l<Tlz. The threshold of hearing varies with frequency.

Figure L2.L.2 shows variation of the threshold of hearing with frequenqr of acertain person. Above the curve represents intensities that canbe detected bythe human ear.Intensities below the curye cannot be detected by the humanear. The sensitivity of the human ear is the ability to detect the smallest

fractional change AI of intensity /. Sensitivity depends on the ratio +SensitMty increases with frequency to a maximum and then decreases withincreasing frequency. The maximum sensitiviry is at 1-3l<Itz.

The human ear can detect a wide range of intensities. The minimumintensrty that can be detected is 1.0 x 10-12Wm-2 at a frequertcy of 3 L<TIz.

The upper limit of the range is 100Wm-2 in the frequency range l kHz to6L<T.12. The upper limit is called the threshold of pain. Persons exposed tointensities of 100W r.rr-2 san experience pain and temporary deafness.

hearingphysics

outerear

: inneni ear

iddt'eear

m

Figure 12.1.7 The human ear

Eq uation

Intensity is the power per unit area

t - * "ra stated frequency.

A

I - intensity/W m-2

P power/WA area/mz

hammerstirrup

Chapterl2 The physics of hearing ffi

The logarithmic response of the earEqual changes in intenstty arc not perceived as equal changes in loudness.

Loudness is the subjective response of a person to a given intensity. Intensitylevel rrray be used as a measure of loudness. Intensity level is defined usingthe following elluation. Changes in loudness depend on the fractional change

in intensity H. Loudness is a logarithmic response to intensity.

ExampleA person with normal hearing is exposed to a sound of frequency 3l<LIzand an intensity level at the ear of 20 dB. Calculate the intensiry of thissound at the ear.

intensityleve[/d B

soundintensity/Wm-2

1.0

10 -2

10 *4

10 -6

10 -8

10 -10

10 -12

120

100

80604020

0

t I\ I\ t\ {

*j1Az 103 104

f lfiz

Figure12.1.2 Variation of threshold ofhearing with frequency

Eq uation

10s10

Intensity level _ 101og,offi)

zo_ 1orog,,(#O=)

los,oF**)I

]-x 10{

1Z-t

lntensity [eve[ =

lntensity levet is(decibets)

I - intensity of sound incident on

ear/W m-z

lo - threshold of hearing(1.0 x 1o-12w r,)

Key points

r The human ear is able to detectfrequencies in the range 20Hzto20kHz.

r The threshotd of hearing is theminimum intensity that can be

detected by the ear.

The sensitivity of the humanear is the abitity to detect thesma[[est fractionaI change A/ ofintensity /.

Loudness is the subjectiveresponse of a person to a giveninte ns ity.

The ear has a logarithmicresponse to sound.

lorog,o[)

measured in dB

I_

100

I x 10-t0wm-2

Loudness and noiseIntensity level is defined in terms of the intensity of sound and thethreshold of hearing at a frequency of 3 kF{rz.

Loudness is the subjective response of a person to a given intensity anddepends on the individual and the frequency of the sound.

To define a consistent unit of loudness, a frequency of l kHz is chosen as

a stand ard. The 1 kHz standard source is adf usted until it is perceived as

being as loud as the source being evaluated. Suppose the intensity level ofthe 1 kHz standard source is found to be 90 dB when it is as loud as thetest source, then the loudness of the test source is 90phons.

Example

The intensity of sound measured at a distance of 0.8m from aloudspeaker is measured as L.2 x 102Wm-2. Given that the intensity

of sound va ' 1 ,rhere d is tkries

^t fu,where d is the distance measured from the

loudspeake4, calculate the intensity of the sound at a distance of 3.0m.

1o<&

kd2

L.Zx 102 _ L(0 8)'

k _ 76.8

Therefore the intenstty at a distance of 3.0 is given by:

I- h_ ffi -8saw',.-z