Lecture 20 Sound

Hearing

Sound Intensity

Sound Level

Doppler Effect

Ultrasound

Applications

Sound Waves

• When a gas, liquid or solid is mechanically

disturbed

− Sound waves are produced

Sound Waves (Longitudinal waves)

Speed of sound in a material depends on

•physical properties of material

----- (e.g. density, temperature)

− When sound encounters a boundary

between substances, some energy is reflected

Reflection makes ultrasound imaging possible

Speed of sound in materials

Material Speed

(ms-1)

Air 344 Gases

Helium 965

Water 1450 Liquids

Blood 1570

Body Tissue 1570 Solids

Copper 3750

Glass 5000

Iron 5000

Sound Waves

In general Vsolids > Vliquids > Vgases

Depends on

•Phase of the material

•Characteristics of the material

(such as density, elasticity & temperature)

•Greater in solids because molecules interact

more strongly with each other

•Greater in rigid materials

Helium has a lower

density than air.

Resonant frequencies of

vocal cavity increase.

Spectral distribution of

sounds shift to higher

frequencies

-timbre of sound changes

Sound Waves

Speed of sound (v)

Ev

Bv

kTv

m

Gas

Liquid

Solid bar E Young’s Modulus

density

p

v

c

c

Cp specific heat constant pressure

Cv specific heat constant volume

m molecular mass

k Boltzmann’s constant

T temperature (Kelvin)

B bulk modulus

Depends

on elasticity and density

kTV

m

Calculate the speed of sound in air at 20 oC

=1.4. Boltzmann’s constant =1.38x10-23J/K

Mass of air molecule = 47.97x10-27kg

23

27

1.4(1.38 10 / )[(20 273.15) ]

47.97 10

J K KV

kg

1343.6V ms

Waves

The speed of sound in water is 4.2 times

the speed of sound in air. A whistle on land

produces a sound wave with frequency f0. When

this sound wave enters water, its frequency is:

a) 4.2f0

b) f0

c) f0/4.2

d) Not enough information given

Speed of sound

The motion of the fluid disturbs hair cells within

the inner ear, which transmit nerve impulses to

the brain corresponding to the sound heard.

Hearing

Ear can detect very low intensity sounds

Ear canal

hammer

ear drum

stirrup

anvil Cochlea

Outer ear Middle Inner ear

Oval window

sound

Sound Waves

Sound wave enters the ear.

Forces exerted on eardrum due to air pressure

variations cause it to vibrate.

three small bones (hammer, anvil, and stirrup)

in the middle ear transmit forces to fluid filled

inner ear (cochlea) through the oval window (small

area compared with eardrum) result pressure x 17

Ear can detect extremely low intensity sounds

Audible sound waves carries very little energy

Power output: Talk ≈10-5W

Talk 24 hours a day non-stop for 114 years

≈106 hours

Total energy output is

≈ (10-5W)(106 hrs) =10 Wh

All waves carry energy

Sound Waves

Equivalent to quantity of energy consumed

by a 100W bulb in 6 minutes

Waves (energy) spread out from source

Intensity (I) of a wave is defined as

•Energy (E) carried per unit time per unit area (A)

/E tI

A E

Pt

therefore P

IA

Power (P)

Unit of intensity: Watt per square metre (Wm-2)

Intensity

Sunlight intensity at Earth ≈103Wm-2

Human ear can detect extremely low intensities

≈10-12Wm-2

Maximum intensity without ear damage ≈1Wm-2

Large range 1012 logarithmic units useful

Sound Waves

Hearing

If we listen to two sounds (I1 and I2)

and I2 seems twice as loud as I1

Human perception

Measure intensities

I2 is approximately 6 to 10 times I1

Convenient scale to measure loudness is

the logarithm of the intensity

Human ear can detect extremely low intensities

≈10-12 Wm-2

Maximum intensity without ear damage

≈1 Wm-2

Large range 1012 logarithmic units useful

Intensity

Ear response to sound

•logarithmic

•not linear

Decibel scale for intensity used

Sound (Intensity) level in decibels (b)

10

0

10logI

Ib

where (threshold of hearing

at 1000Hz)

12 2

0 10I Wm

decibel (b) is a relative sound level measurement

Perceived loudness is roughly Logarithmic

Threshold of discomfort = 1 Wm-2

Above this pain is experienced and there is

potential for long term damage

Sound Waves

Hearing

Sensitivity of ear Can detect sound intensity of ≈10-12Wm-2

Corresponds to pressure variation of ≈ 3x10-5 Pa

(Atm. Pressure ≈ 101,325 Pa)

Random fluctuation due to thermal motion

of molecules ≈ 5x10-6 Pa

Sensitivity:

essentially due to mechanical layout

•Area ratio: ear drum to oval window ≈ 17

•hammer, anvil and stirrup amplification ≈2

•canal resonance at 3kHz pressure increase ≈2

•Total pressure amplification ≈ 17x2x2 = 68

2( )Intensity pressure

Intensity increases by factor of 682=4624

Brain: discriminatory role

Filters unwanted noise

Suppression: non-awareness of background noise

ear is not equally sensitive at all frequencies

Sound level

(dB)

Intensity

(Wm-2)

Sounds

0 1x10-12 Threshold of hearing

10 1x10-11

20 1x10-10

30 1x10-9 Quiet home

40 1x10-8 computer

50 1x10-7

60 1x10-6 Normal conversation

70 1x10-5 Busy traffic

80 1x10-4 Loud radio

90 1x10-3

100 1x10-2

110 1x10-1

120 1 Rock concert

140 1x102 Jet airplane at 30m

160 1x104 Bursting eardrums

Sound levels and Intensities

Sound Waves

10

0

10logI

Ib

Computer 10 times louder than quiet room

Does not seem so because of the logarithmic

response of the ear

Sound levels and Intensities

Damage Threshold

5 hours/week at > 89dB

damage after 5 years

> 100dB deemed hazardous

D a n g e r H e a r i n g l o s s

10 minutes at 120dB

Temporarily changes your threshold of hearing

from 0dB to 30dB

(a) Calculate the sound level in dB of a sound

intensity 10-8Wm-2

(b) Calculate the intensity in Wm-2 of a sound

level of 80 dB

(a) 10

0

10logI

Ib

8 2

10 12 2

1010log

10

Wm

Wmb

(b) 10

0

80 10logI

I

Sound Waves

8 12 2 4 2

4 2

10 10 10

10

I Wm Wm

I Wm

10

0

8 logI

I

8

0

10I

I

4

1010log 10 10 4 40db b

Ability to hear is not only a function of

intensity but also frequency

Intensity hearing range: 10-12Wm-2 →1Wm-2

0 → 120 dB

Frequency range: 20 Hz → 20 kHz

Hearing ability

Loudness is a method of describing the acoustic

pressure (or the intensity) of a given sound

Dogs: up to 50 kHz

Dolphins: up to 250 kHz.

Bats: up to 120 kHz

Humans

Sound Waves

Hearing ability as a function of intensity and

frequency. The blue solid line is the pure tone

threshold curve, below which the subject does

not hear.

Ear most sensitive at 3000 Hz

Pain threshold almost frequency independent

Sound Waves

20 10 1k 10k 20k Hz

frequency

Intensity

Level

dB

120

100

80

60

40

20

0

Intensity

W/m2

100

10-2

10-4

10-6

10-8

10-10

10-12

Pain threshold

Hearing threshold

Hearing ability

Waves

A bat can hear sound frequencies up to

120,000 Hz. What is the wavelength of sound

in the air at this frequency?

v f

13344

2.87 10120,000

v msmetres

f Hz

=.287cms

v

f

High frequency—short wavelength

Wave only disturbed by objects with dimensions

similar to or greater than the wavelength

Smaller objects have little effect

Bats use ultrasound for navigation

Can distinguish between insect and falling leaf

Example

Traveling waves transfer energy from one

place to another

Sound Waves

Examples

• foghorns have a low frequency

•Elephants communicate over long distances

(up to 4 km), frequencies as low as 14 Hz

Sound energy dissipates to thermal energy

when sound travels in air.

Higher frequency sounds dissipate more quickly,

so lower frequency sounds travel further.

Change in observed frequency depends on the

relative motion of the source and observer.

Occurs with all types of waves – most notable

•sound waves,

•light waves.

Doppler Effect

stationary

moving→

Perceived pitch (or frequency) of a moving sound

source changes as it goes past

Christian Doppler 1803-1853

Austrian Physicist, Mathematician

Longer

Lower f

Shorter

higher f

Sound Waves

Waves

Observed frequency for a moving source

+ sign: source moving away from observer

- sign: source moving towards observer

Stationary source, moving observer

wave observerobserver source

wave

v vf f

v

- sign: observer moving away from source

+sign: observer moving towards source

f = Frequency

v = Speed

waveobserver source

wave source

vf f

v v

Waves

Example: Moving Source

A police car with a 1000 Hz siren is moving at

20 ms-1. What frequency is heard by a

stationary listener when the police car is:

a) Moving away from

b) approaching the listener

(a) wave

observer source

wave source

vf f

v v

1

1 1

3441000 1062

344 20observer

msf Hz Hz

ms ms

(b)

1

1 1

3441000 945

344 20observer

msf Hz Hz

ms ms

waveobserver source

wave source

vf f

v v

Waves

Example (moving observer)

A stationary siren has a frequency of 1000 Hz.

What frequency will be heard by drivers of cars

moving at 15 ms-1?

a) away from the siren?

b) toward the siren?

(a) w oo s

w

v vf f

v

w oo s

w

v vf f

v

1 1

1

344 151000 956

344o

ms msf Hz Hz

ms

(b)

1 1

1

344 151000 1044

344o

ms msf Hz Hz

ms

Waves

waveobserver source

wave source

vf f

v v

Doppler effect can be used to measure speed

Radar measures Doppler shift to determine

speed of car

•compares frequency of reflected wave from car

and with that emitted from source

Similarly ultrasound can measure blood speed,

fetal heart motion.

Frequency greater than range of human hearing

Sound with frequencies above 20 kHz

Ultrasound

• Diagnostics

• Therapeutic

• Quality control

Normally 1 MHz→20MHz

•Doppler effect with ultrasound can be used to

detect fetal heart beats

• pulsation of artery walls

Ultrasound

Medical applications

Reflections of ultrasound pulses from patients

occur at interfaces between different tissues

Ultrasound probe passed over region of interest

Reflection time provides depth information

Image constructed from echo

and position information

Medical ultrasound without harmful effects

•intensity kept low (≈10-2 Wm-2) to avoid tissue

damage

Good contrast: reflected from boundaries

between materials of nearly the same density

Ultrasound scanning during pregnancy

Auto-focusing cameras

computes time taken (and hence distance

of subject) for the reflected ultrasonic sound

wave to reach the camera lens position and

then sets focus accordingly.

Ultrasound

Other uses in medicine

• Destructive effects

− Intense ultrasound produces large

density and pressure changes

• Results

− Large stresses

− Molecules are forced to move rapidly

− Heat is produced in most materials

− Bubbles of vapour are formed

(cavitation)

Ultrasound

•Non destructive method for measuring enamel

thickness, pulse-echo measurements

Measurement of dental erosion

Dental applications

It consists of a ultrasound probe with a small

tip. The ultrasound in combination with water

flow effective in plaque and tartar removal

Plaque, film of food and bacteria, builds up

on teeth. Not removed, it hardens into tartar.

ultrasonic scalar

Teeth cleaning

Example

Ultrasound speed =1500m/s in tissue.

Using an ultrasound frequency of 2MHz,

calculate (a) smallest detail visible

(b) time for reflected wave to return to probe

from a depth of 10cm

v f 6

1500 /

2 10

v m s

f Hz

(a)

(b) time for reflected wave to return to probe

4

1

2 0.101.3 10 sec

1500

s mt

v ms

Ultrasound

= 0.75mm

Why use ultrasound---not audible sound

Smallest detail observable ≈ one wavelength