Upload
lykien
View
222
Download
0
Embed Size (px)
Citation preview
Lecture 1 Sound
Hearing
Sound Intensity
Sound Level
Assistant Prof. Matthias Möbius
Sound Waves
Gas, liquid or solid is mechanically disturbed
• Sound waves are produced
Speed of sound in a substance depends on
•physical properties
•e.g. (density, temperature)
When sound encounters a boundary between
substances,
some sound energy is
transmitted and some reflected
Reflection makes ultrasound imaging possible
rarefaction compression
De
nsity o
f A
ir
Compressed air >>> increased pressure
Rarefied air >>> reduced pressure
organised vibrations of air molecules>> sound
A plucked string will vibrate at its natural
frequency and alternately compresses and
rarefies the air alongside it.
Sound
Sound Waves (Longitudinal waves)
direction
Sound
Sound waves-(variation in air pressure)
can cause objects to oscillate
Example: ear drum is forced to vibrate in
response to the air pressure variation
Depending on:
intensity of the sound
frequency of vibration
movement of the ear drum will
stimulate nerve cells and the sound will be
perceived.
Speed of sound (v) in materials
Material Speed (ms-1)
Air 344
Helium 965
Water 1450
Blood 1570
Body
Tissue
1570
Copper 3750
Iron 5000
Glass 5000
•Greater in solids because molecules interact
more strongly with each other
•Greater in rigid materials
Sound Waves
In general
Depends on
•Phase of the material
•Characteristics of the material
(elasticity, density & temperature)
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
solids liquids gasesv v v
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
Avg. 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
Sound
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
• Frequency (f) of a wave is independent
of the medium through which the wave
travels.
–It is determined by the frequency of the
oscillator that is the source of the waves.
Diffraction
Sound
Light waves:
•Wavelengths « dimensions of everyday objects
•Little diffraction occurs
•Relatively sharp shadows occur
Sound waves:
• Wavelength ≥ size of everyday objects
•diffraction occurs
Example
Sound
source
134434.4
1
v mscm
f KHz
Longer the wavelength compared
to size of opening or object the
greater the diffraction
8 1
14
3 10500
6 10
v msnm
f Hz
The motion of the fluid disturbs hair cells within
the Cochlea, 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
Hearing
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 amplify & transmit forces to fluid filled
inner ear through the oval window (very small
area compared with eardrum) result pressure x 30
Other amplification characteristics ??
Ear can detect extremely low intensity sounds
Audible sound waves carries very little energy
Power output: Talk ≈10-5 W
Talk 24 hours a day non stop for 114 years
≈106 hours
Total energy output is ≈10-5 w x106 hrs =10 Wh
All waves carry energy
Hearing
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 ≈103 Wm-2
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
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
Hearing
Logarithm is the inverse of exponentiation:
Note that logarithms can have different bases.
The most common ones are:
log10, log2, ln (natural logarithm with base e)
log(a b) = log(a) + log(b)
log(a/b) = log(a) - log(b)
log(ab) = b log(a)
log(1) = 0 for all bases
Convert between different bases:
logx(A) = logy(a) / logy(x)
Logarithm
10x =120
log10 (10x) = log10 (120)
x log10 (10) = log10 (120)
x=log10 (120)
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 ≈ 30
•hammer, anvil and stirrup amplification ≈2
•canal resonance at 3kHz pressure increase ≈2
•Total pressure amplification ≈ 30x2x2 = 120
2( )Intensity pressure
Intensity increases by factor of 1202=14,400
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 room
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, Threshold
of pain
140 1x102 Jet airplane at 30m
160 1x104 Bursting eardrums
Sound levels and Intensities
Computer 10 times louder than quiet room
Does not seem so because of the logarithmic
response of the ear
Vibration
amplitude.
air molecules
1.1x10-11m
1mm
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
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 40 kHz
Dolphins:
up to 250 kHz.
Bats:
up to 120 kHz
Humans:
Hearing
Infrasonic < 20 Hz 20 kHz < ultrasonic
Elephants:
down to 1Hz
Pigeons:
down to 0.1 Hz
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
Hearing
20 100 1k 10k 20k Hz
frequency
Sound
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
Human Hearing Ability
Why two ears
Time difference of sound arriving at both ears
used to locate the source of the sound
Hearing
Sounds from different directions arrive at each
of our ears at slightly different times and with
slightly different intensities.
Main advantage
Other advantages
•easier to understand speech in noisy background
• help judge loudness
Example:
crossing a road
direction of the car
approximately how close it is
Inverse Square Law
Distance
powerIntensity
area
1 2
14
PI
r 2 2
24
PI
r
2
1 2
2
2 1
I r
I r
Consider imaginary spheres
r2
r1
Isotropic
source
Sound intensity is reduced by moving away
from source By how much?
As the person gets further away, the sphere that
intersects with them gets larger and larger
Fraction = Area of person 4 π r12
Fraction = Area of person 4 π r22
Sound intensity
Inverse square law
2
1 2
2
2 1
I r
I r
Variation of Sound Intensity with
distance from a point source
Intensity I1 at a distance r1 from source
Intensity I2 at a distance r2 from source
Intensity is inversely proportional to the
square of the distance from the source.
NOTE: Sound level (dB) is not inversely
proportional to distance squared !
Sound intensity
A person near a source of loud noise wants to
decrease their exposure to it by a factor of 10.
How far away do they have to move?
2
1 2
2
2 1
I r
I r
2
1 2
21 1
10
I r
I r
2
2
2
1
10r
r 2
1
10 3.16r
r
They have to move 3.16 times further away
The intensity falls off as 1/r2 (where r is the
distance) so moving 4 times as far away will
decrease the exposure by a factor of 16.
Examples
Sound intensity
Waves
A bat can detect 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
Waves
Resonance
Most objects have a natural frequency:
Determined by
• size
• shape
•composition
If an object is subjected to an intense wave
oscillating at object’s natural frequency
a large response (Resonance) occurs
Resonance occurs if
frequency of the driving force equals
natural frequency of the system
Example: child being pushed on a swing.
Swing is kept in motion at its natural frequency
by a series of appropriately timed pushes.
Difficult to get it to swing at any other frequency
12
lT
f g
Simple pendulum
Only one natural frequency
Waves
Resonance: examples
Roman foot soldiers were instructed to break step
when marching over a bridge
•Prevented possible resonance response and
bridge damage
Opera singers with powerful voices
can set glasses into audible vibration
If frequency of note is the same as the natural
frequency of the glass, the glass may vibrate
with a large amplitude and may break
Air passages of the
mouth,
larynx
Nasal cavity
together form an acoustic resonator.
Voiced sound depend on
•resonant frequencies of the total system
------depends on system’s volume and shape
Resonance: examples
Electrical Resonance:
Example: Tuning in radio station
Adjust resonant frequency of the electrical circuit
to the broadcast frequency of the radio station
To “pick up” signal
Half-closed pipe Resonance (e.g. ear canal):
/f soundsonanceRe
)L4/(f sound1 Fundamental mode:
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,
because more energy transferred to the medium;
so lower frequency sounds travel further.
Travel distance is a function of frequency
Lecture 2 Sound
Beats
Doppler Effect
Ultrasound
Applications
Waves
Beats If the two waves interfering have slightly
different frequencies (wavelengths), beats occur.
In step (in phase) In step (in phase)
Out of step (out of phase)
Superposition Simple case: Addition of two waves with
same frequency and amplitude
Wave 1
Wave 2
resultant
Waves
Beats If the two waves interfering have slightly
different frequencies (wavelengths), beats occur.
fb = f1-f2
Waves get in and out of step as time progresses
Result-
• constructive and destructive interference occurs
alternately
•Amplitude changes periodically at the beat
frequency Beat frequency
Absolute value: beat frequency always positive
Wave 1
Wave 2
Resultant
envelope
Waves
Beats fb = f1-f2
No beats occur
If frequency difference = zero
Wave 1
Wave 2
resultant
Waves
Beats
Sound waves Beats perceived as a modulated sound:
loudness varies periodically at the beat frequency
Application
Accurate determination of frequency
Piano tuning
Adjust tension in wire and listen for beats
between it and a tuning fork of known frequency
The two frequencies are equal when the beats
cease.
Easier to determine than when listening to
individual sounds of nearly equal frequencies
f1 = 264Hz
f2 = 266 Hz
Beat frequency 2Hz
Beats can happen with any type of waves
Example
Change in perceived frequency depending on
the relative motion of the source and listener.
Occurs with all types of waves – most notable
•sound waves,
•light waves.
Doppler Effect
stationary
moving→
Example:
Perceived pitch (or frequency) of a moving
source such as a fire engine siren changes as it
goes past
Christian Doppler 1803-1853
Austrian Physicist, Mathematician
Longer
Lower f
Shorter
higher f
Sound Waves
Frequency of sound emitted does not change
Waves
Doppler effect is observed because the distance
between the source of sound and the observer
is changing.
source always emits the same frequency.
Source moving towards the observer
•sound waves reaching observer perceived to
be at a more frequent rate (higher frequency)
sound waves compressed into shorter distance
Source moving away from the observer,
•sound waves reaching observer perceived to
be at a less frequent rate (lower frequency)
Sound waves expanded into longer distance
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 observer
A stationary siren has a frequency of 1000 Hz. What
frequency will be heard by drivers of cars moving at 15ms1?
a) away from the siren?
b) toward the siren?
(a) w o
o 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
wave observerobserver source
wave
v vf f
v
Example: Moving Source
A Garda 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) waveobserver 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
If you were to replace the Garda car with 2 stationary
sirens emitting at the two frequencies as perceived in (a)
and (b), what would be the beat frequency between them?
Beat frequency beat a bf f f
945 1062beatf Hz Hz
117beatf Hz
Waves
Doppler effect can be used to measure speed
of the source
Police radar uses radio waves:
measures Doppler shift to determine speed of car
•compares frequency of reflected wave from car
with that emitted from radar
Radar: RAdio Detecting And Ranging
Doppler RADAR
•Weather
•Rainstorms, tornadoes
•Wind sheer at airports Swirling air & water droplets
RADAR
Wave source
Sound Waves
Reflection of waves (echoes)
•Caused by solid object
•Change in nature of medium
- Underwater navigation and observation
Sound waves applications
SONAR (sound navigation and ranging)
• Measuring the travel time of sound waves
in the ocean can help monitor sea
temperatures and global changes
Frequency greater than range of human hearing
Sound with frequencies above 20 kHz
Ultrasound
Applications
•Navigation
•Diagnostics
•Surgery
•Therapeutic
•Cleaning
Normally 1 →20MHz
Typical prey: moths (dimensions cms)
Bats use ultrasonic echolocation methods to
detect their presence.
Bats can determine distance, speed and direction
of their prey
(using reflection time and Doppler effect)
why do bats use ultrasound?
13344
6.88 10 0.750
v msm cm
f kHz
Ultrasound- Shorter wavelength
•Reflection, not diffraction occurs at moth.
Submarines, dolphins and bats use ultrasound
for navigation 30-100kHz
13344
344 10 34.41
v msm cm
f kHz
Audible
Ultrasound
Ultrasound
Ultrasound
Medical applications
Reflections of ultrasound pulses from patients
occur at interfaces between different tissues
of different density
Ultrasound probe passed over region of interest
Reflection time provides depth information
Image constructed from echo
and position information
Good contrast: reflection from boundaries
between materials of nearly the same density
Ultrasound Imaging
Ultrasound & Doppler effect
can be used to measure
• Blood flow speed in arteries and veins,
measure arterial occlusion
•Echocardiogram , examination of the heart
• measure blood flow in and out
•fetal heart beats
• pulsation of artery walls
Medical applications
Stroke: early warning
Monitor blood speed in carotid artery in neck
Ultrasound
Red blood cell
Ultrasonic Doppler flow meter Transmitter Receiver
Ultrasound
•intensity kept low (≈10-2 Wm-2) to avoid tissue
damage
Ultrasound scanning during pregnancy
Medical ultrasound without harmful effects
Surgery
Ultrasonic scalpel (55kHz)
Precise cutting and coagulation
•Tumour removal
•Tonsillectomies
Imaging
Why use ultrasound---not audible sound
Smallest detail observable ≈ one wavelength
Ultrasound
Compromise between spatial resolution of image
and penetration depth
•Frequency is selected based on the depth
of the tissue to be treated.
Example: deep heat therapy (low frequency)
115700.5
3000
v msm
f Hz
115701
150
mscm
kHz
Audible sound wavelength in tissue
Ultrasound wavelength in tissue
In tissue, higher frequencies are attenuated more
1MHz:
penetration depth ≈ 6cm
3MHz: superficial conditions (eg. Tennis elbow etc)
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 5cm
v f 6
1500 /
2 10
v m s
f Hz
(a)
(b)
time for reflected wave to return to probe
5
1
2 0.056.6 10 sec
1500
s mt
v ms
Ultrasound
l = 0.75mm
Ultrasound
•Destructive effects
•Intense ultrasound produces large
density and pressure changes
• Results
− Large stresses
−Heat is produced in most materials
− microscopic vapour bubbles formed and
implode releasing energy (cavitation)
Non-invasive removal of kidney stones
Dental applications
Consists of a ultrasound probe with a small
tip. The ultrasound in combination with water
flow effective in plaque and tartar removal
ultrasonic scalar
Other uses in medicine
Ultrasound
Auto-focus 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.
Component surface cleaning
Component placed in fluid in ultrasonic bath
Ultrasound creates a periodic compression
and expansion in the fluid.
Bubbles formed, grow, and implosively collapse
Results in Acoustic cavitation
localised heating (>1000K)
and high pressures (>100 atmospheres)
Result: effective surface cleaning
Sound
Moving source, approaching listener
When speed of source approaches the speed of
sound, waves ahead of source come close
together.
Supersonic speed
waveobserver source
wave source
vf f
v v
observerf approaches infinity
Nearly infinite number of wave crests reach
observer in very short time
is known as a shock wave
source wavev vWave front produced when
sonic boom
At supersonic speeds the waves overlap and
there are many points of constructive interference,
shock wave results
Sound
Supersonic speed
0sv
sv v
supersonic
subsonic
sv v
sv v
Mach 1
Waves ahead of source
come closer together
Waves pile up at front
Waves overlap:
Shock wave,
Sonic boom.
Stationary source v = 0
Circles represent wave fronts
emitted from sound source
Speed of sound in air =vs
Sound
Supersonic speed
sin sv t
vt
1
sins
vM
v
sin 1 since No shock unless
1M
vt
sv t
Sound wave travels a distance vst
Source travels distance vt
In time interval t
Tangent lines lie on surface of cone
Ratio is called Mach number M s
v
v
sv v
Circles represent wave fronts
emitted from sound source
object speedM
speed of sound
Bow
Waves
sin wwv t
vt
Speed of boat v
> Water wave speed Vww
What is the speed of ultrasound with a wavelength of
0.25 mm and a frequency of 6 MHz? How does this
compare with the speed of sound in air?
Question
v f
6 3 3 16 10 0.25 10 1.5 10v Hz m ms
3 1
1
1.5 104.4
344
ms
ms
Compare with speed of sound in air
Lightening strikes 10 km away.
(a) How long after the strike will you see the light?
(b) How long after the strike will you hear the sound?
c = 3*108 m/s, s = 10 km, t = ? (a)
(b) v = 344 m/s, s = 10 km, t = ?
s = vt t = s/v = (10,000 m)/(344 m/s) = 29 s
s = vt t = s/v
t = (10,000 m)/(3*108 m/s) = 3.3*10-5 s
If you hear the sound 3 seconds after you see
the lightening how far away is the strike?
s = vt =(344 m/s)(3 s) = 1002 m
Question
(a) What is the sound level in decibels of a sound with an
intensity of 0.0200W/m2?
(b) If you had 3 such sounds what would the sound level
be?
10
0
10logI
Ib
2 2
10 12 2
2 1010log
10
Wm
Wmb
10
1010log 2 10b 10 1010 log 2 10 log 10b
10 0.3 10b 103dBb
Question
(a)
(b) 2 2
10 12 2
3 2 1010log
10
Wm
Wmb
10
1010log 6 10b
10 1010 log 6 10 log 10b
10 0.78 10b
107.8dBb
Not equal to 3x103 dB !
Sound levels are logarithms of intensity