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TRANSCRIPT
Sound Generation Energy is transmitted as a pressure wave.
There is no net motion of the medium.
The medium oscillates in simple harmonic motion.
The frequency of the wave is the same as the vibrating source.
Vibrating
String
Spherically Symmetric
Sound Source (bell).
Representations of Waves
• Wave fronts are the concentric arcs
– The distance between successive
wave fronts is the wavelength
• Rays are the radial lines pointing
out from the source and
perpendicular to the wave fronts
• Far away from the source, the
wave fronts are nearly parallel
planes
• The rays are nearly parallel lines
Echo vs Reverb
A reverberation is perceived when the reflected sound wave reaches your ear in less than 0.1 second after the original sound wave. Since the original sound wave is still held in memory, there is no time delay between the perception of the reflected sound wave and the original sound wave. The two sound waves tend to combine as one very prolonged sound wave.
Diffract We can hear around corners.
Why can’t we see around corners?
If the size of the wave (wavelength) is close in size to the
object (door way) then the wave will diffract (bend).
Refract Sound waves refract (bend) when moving between
mediums in which it travels at different speeds.
343 m/s in Air @ 20 C
5960 m/s in Steel @ 20 C
1522 m/s in Ocean Water @ 20 C
Speed of Sound in a Vacuum?
Speed of Sound: Temperature
C(331 m/s) 1273 C
Tv
WARNING!
Some textbooks and teachers mistakenly state that the speed of sound increases with increasing density. This is usually illustrated by presenting data for three materials, such as air, water and steel. With only these three examples it indeed appears that speed is correlated to density, yet including only a few more examples would show this assumption to be incorrect. All other things being equal, sound will travel more slowly in denser materials, and faster in stiffer ones.
Bv
elastic property
inertial propertyv
Yv
Fv
Speed of Sound: Medium
All other things being equal, sound will travel more slowly in
denser materials, and faster in stiffer ones.
For instance, sound will travel faster in iron than uranium,
and faster in hydrogen than nitrogen, due to the lower density
of the first material of each set. At the same time, sound will
travel faster in iron than hydrogen, because the internal
bonds in a solid are much stronger than the gaseous bonds
between hydrogen molecules. In general, solids will have a
higher speed of sound than liquids, and liquids will have a
higher speed of sound than gases – not because of greater
density, but stronger bonds!
Toy Model
The transmission of sound can be illustrated by using a toy model consisting of an array of balls interconnected by springs. For real material the balls represent molecules and the springs represent the bonds between them. Sound passes through the model by compressing and expanding the springs, transmitting energy to neighboring balls, which transmit energy to their springs, and so on. The speed of sound through the model depends on the stiffness of the springs (stiffer springs transmit energy more quickly). In a real material, the ‘stiffness of the springs’ is called the elastic modulus, and the mass corresponds to the density. All other things being equal, sound will travel more slowly in denser materials, and faster in stiffer ones.
elastic property
inertial propertyv
Bv
Yv
• The speed of sound waves in a medium depends on
the elasticity, density and temperature: decreases with
increasing density and increases with Temperature!
• The compressibility can be expressed in terms of the
elastic modulus of the material:
Bv
elastic property
inertial propertyv
Yv
Liquid or Gas:
1-D String: Fv
Solid Rod:
Speed of Sound: Medium
All other things being
equal, sound will
travel more slowly in
denser materials, and
faster in stiffer ones.
i
Fvolume stress AB
Vvolume strainV
Train #1
It is possible to hear an approaching train
before you can see it by listening to the
sound wave through the track. If the elastic
modulus is 2.0 10^11 N/m^2 and the
density of steel is 7.8 10^3 kg/m^3,
approximately how many times faster is the
speed of sound in the track than in air?
Periodic Sound Waves
s (x, t) = smax cos (kx – t)
P = Pmax sin (kx – t)
Pressure Amplitude: variation in gas pressure
Displacement amplitude of the wave:
smax is the maximum position from the
equilibrium position:
2
max max
/( ) sin( ) sin( )
/ /i i
Stress F A P A s sB P B B v ks kx t v s kx t
Strain V V V V A x x
The pressure wave is 90 out of phase with the displacement wave
max maxP v s
#2 Pressure Wave Problem
The variation in the pressure of helium gas,
measured from its equilibrium value, is
given by
P = 2.9 10–5 cos (6.2x – 3000t)
where x and t have units m and s, and P is
measured in N/m2. Determine the
frequency (in Hz), the wavelength, (in m)
and the speed (m/s) of the wave.
The power transmitted through a closed surface by a wave is
proportional to the amplitude of the wave.
Sound Power
EQUATION DANGER!!!!
2 2
max
1
2A s v
Power Transmitted on a String: 2 21
2A v
Power Transmitted by Sound:
NOTE: A’s are not the same!!!!!!
maxSound: A Area s Amplitude
String: A Amplitude
2
W
mI
A
The intensity of a wave, the power per unit area, is the rate at
which energy is being transported by the wave through a unit
area A perpendicular to the direction of travel of the wave:
22 max
max
1( )
2 2
PI v s
v
Spherical Waves
• A spherical wave propagates radially outward from the oscillating sphere
• The energy propagates equally in all directions
• To compare intensities at two locations, the inverse square relationship can be used
2
1 2
2
2 1
I r
I r
2 2
W
4 m
av avIA r
#3 Intensity
A point source emits sound with a power output of
100 watts. What is the intensity (in W/m2) at a
distance of 10.0 m from the source?
2 2
W
4 m
PI
r
0
10 logI
dBI
12 2
0Threshold of hearing : 10 /I W m
Decibel Index:
Whisper: 20db
Conversation: 60db
Loud Music: 120 db
Jet: 140 dB
Rocket: 250dB
At 90db, wear ear plugs!!!
12 2
0Threshold of hearing : 10 /I W m
4 2Bursting of eardrums : 10 /I W m
6 2Normal Conversation: 10 /I W m
10 2Whisper: 10 /I W m
2
0
10
WhisperI
I
0
log 2WI
I 2 bels
10 1decibels bel 20 decibels
0 dB
20 dB
60 dB
160 dB
0
10 logI
dBI
OSHA Safety Standards
OSHA - Occupational Safety and Health Act - The OSHA criteria document reevaluates and reaffirms the Recommended Exposure Limit (REL) for occupational noise exposure established by the National Institute for Occupational Safety and Health (NIOSH) in 1972. The REL is 85 decibels, A-weighted, as an 8-hr time-weighted average (85 dBA as an 8-hr TWA). Exposures at or above this level are hazardous.
Whisper: 20db
Conversation: 60db
Loud Music: 120 db
Jet: 140 dB
Rocket: 250dB
At 90db, wear ear plugs!
You Try
#3, again. A point source emits sound with a power
output of 100 watts. What is the intensity (in
W/m2) at a distance of 10.0 m from the source in
dB?
0
10 logI
dBI
2 2
W
4 m
PI
r
11
0
10 logI
dBI
4. If a sound is twice as intense, how much greater is the
sound level, in db?
22
0
10 logI
dBI
2 12 1
0 0
10 log 10 logI I
dB dBI I
2 12 1
0 0
10 log /I I
dBI I
2
1
10 logI
dBI
2 1 10 log2dB
3.01dB
53 dB is twice as intense as 50dB. Log Scale!!
Quiz: Increasing the intensity of sound
by a factor of 100 causes the sound
level to increase by what amount?
1. 100dB
2. 10dB
3. 20dB
4. 200dB
5. 2 dB
22
1
10 logI
dBI
2 10 log 100 10 2 20dB x
11
0
10 logI
dBI
#5. The decibel level of a jackhammer is 130 dB relative
to the threshold of hearing. Determine the sound intensity
produced by the jackhammer.
1
0
130 10 logI
dB dBI
1
0
13 logI
I
1
0
log1310 10
I
I
13 1
0
10I
I
13
1 010I I 13 1210 10 210 /W m
You Try
6. Calculate the intensity level in dB of a sound
wave that has an intensity of 15 10–4 W/m2.
a. 20
b. 200
c. 92
d. 9
e. 10
0
10 logI
dBI
2 2
W
4 m
PI
r
You Try
7. By what factor will an intensity change when the corresponding sound level increases by 3 dB?
a. 3
b. 0.5
c. 2
d. 4
e. 0.3
0
10 logI
dBI
2 2
W
4 m
PI
r
is a What you Hear
The Pressure Wave sets the Ear Drum into Vibration.
The ear converts sound energy to mechanical energy to a nerve impulse which is transmitted to the brain.
Drum to Stirrup: Simple Machine
Amplification Since the pressure wave striking the large area of the eardrum is concentrated into the smaller area of the stirrup, the force of the vibrating stirrup is nearly 15 times larger than that of the eardrum. This feature enhances our ability of hear the faintest of sounds.
Resonance of the Cilia Nerves The inner surface of the cochlea is lined with over
20 000 hair-like cilia connected to nerve cells, each differing in length by minuscule amounts. Each hair cell has a natural sensitivity to a particular frequency of vibration. When the frequency of the sound wave matches the natural frequency of the nerve cell, that nerve cell will resonate with a larger amplitude of vibration which induces the cell to release an electrical impulse along the auditory nerve towards the brain.
Cochlear Cilia Nerve Damage
Normal Ear Damaged Ear
Excessive exposure to loud sound can damage your cilia.
Sonic: 20 Hz 20 kHz
INFRAsonic: 20Hz
ULTRAsonic: 20kHz
f
f
A middle C vibrates 252 times per second.
Sound Frequencies
Scientists first detected infrasound in
1883, when the eruption of the
Krakatoa volcano in Indonesia sent
inaudible sound waves careening
around the world, affecting barometric
readings. 310dB estimated
The eruption of the Fuego volcano in
Guatemala last year generated high-
amplitude infrasound, mostly below 10
hertz. The pressure readings show that
the strength of these sound waves can
reach the equivalent of 120 decibels.
Infrasonic: < 20Hz
Ultrasound
Intensity of reflected sound wave (echo) is
related to change in density in target.
Ultrasound beam:
-2
7 1 detail
~ 10
MHz mm
I W
"A Womb With a View" and
"Fetal Fotos” “Peek in the Pod”
Hi Cost Hi-Definition Ultrasound
Are there RISKS?
"We do know in animal
studies, certain levels of
ultrasound can cause
damages in growing bones,
in developing bones," said
Dr. Dan Schultz of the Food
and Drug Administration.
Ultrasound Question 8. How far apart are two layers of tissue that produce echoes
having round-trip times that differ by 0.750s? What minimum
frequency must the ultrasound have to see detail this small?
The speed of sound in human tissue is 1540m/s.
6
4w1540 m s 0.750 10 s
5.78 10 m2 2
v td
v f fv
ww 6m s
m2.67 10 Hz
1540
578 10 4.
2 1 s 2 s 1 s / 2d d d v t v t v t
Animal Perception of Sound
•domestic cats •100-32,000 Hz
•domestic dogs •40-46,000 Hz
•African
elephants •16-12,000 Hz
•bats •1000-150,000
Hz
•rodents •70-150,000 Hz
Human: 20-20,00Hz
Infrasonic Contact Calls
Female African elephants use "contact calls" to communicate
with other elephants in their bands (usually a family group).
These infrasonic calls, with a frequency of about 21 Hz and a
normal duration of 4-5 seconds, carry for long distances (several
kilometers), and help elephants to determine the location of
other Elephants. Calls vary among individual elephants, so that
others respond differently to familiar calls than to unfamiliar
calls. Perhaps elephants can recognize the identity of the caller.
Echolocation: Sonic Vision
Dolphins produce high frequency (100kHz) clicks that pass through
the melon. These sound waves bounce off objects in the water and
return to the dolphin in the form of an echo. The brain receives the
sound waves in the form of nerve impulses. By this complex system
of echolocation, dolphins can determine size, shape, speed, distance,
direction, and even some of the internal structure of objects in the
water.
Dolphin
Vocalization
SOund Fixing And Ranging
Acoustic Thermometry of Ocean Climate
ATOC: 70 Hertz, with a sound pressure level of 195 dB
Dolphin, pinniped species sensitive to high frequencies (above 10,000 Hz)
Baleen whales sensitive to low-frequencies (below 100 Hertz)
SOFAR Channel
The LFAS system consists of a 35-
ton block of 18 huge underwater
speakers and dozens of
microphones. The speakers emit a
consistent low-frequency tone,
between 100 and 500 Hertz, at
240dB, which travels out into the
water at a depth of several hundred
meters. The low frequency permits
the sound to travel tremendous
distances, detecting objects many
hundreds of miles away by
echolocation.
At 100 mile radius from the ship the noise only drops to
160 db which causes shearing of the tissues in the air
sack behind whales' and dolphins' brain. This air sack is
highly sensitive since it is used in echolocation.
“Sound bombing" of ocean floors
to test for oil and gas for National
Security?
2004: More than 100 whales and dolphins died in two separate
beachings in 24 hours on remote Australian islands after US and
Australian navies sound bombed the ocean nearby.
Sea Quakes produce
powerful pressure
waves that rupture
the sinuses and
middle ear of whales
and dolphins.
•Cosmological Redshift: Expanding Universe
•Stellar Motions: Rotations and Radial Motions
•Solar Physics: Surface Studies and Rotations
•Gravitational Redshift: Black Holes & Lensing
•Extra-solar Planets via Doppler Wobbler
S O ?v
Speed of a wave is determined
by the properties of the Medium!
Case 1: Moving Source Stationary Observer 0Ov
What is the speed of sound to the observer?
wavev v
S O
Speed of a wave is determined
by the properties of the Medium!
Case 1: Moving Source Stationary Observer 0Ov
What is the speed of sound to the observer?
v v
wavev v
What is wavelength and frequency to the observer?
, f f
Sv
is shortened by
= Sv
Case 1: Moving Source Stationary Observer 0Ov
= (1 )Sv
v
= (1 )Sv
v
= (1 )Sv
= ( )sv v
v
?f
Case 1: Moving Source Stationary Observer 0Ov
Use v v
= sv v
v
( )s
f f fv v
v
'f f
1
1 S
f fv
v
Sv
What if ?Sv v
When the duck speed is equal or greater than
the speed of waves in water, the waves form a bow wave.
Case 2: Observer Moving & Stationary Source
S Ov
Observer Moving TOWARD (+) and
AWAY (-) from Source
ov vf f
v
ov v v
0(1 )v
f fv
In Sum, if both Source and Observer
are moving…..
sound
observer
source
o
s
O
S
v vf f
v v
v
v
v
0(1 )v
f fv
1
(1 )S
f fv
v
Only Source Moving: Only Observer Moving:
Both: The signs depend on
the relative motion.
For the velocity:
Moving away: minus
Moving toward: plus
Doppler Shift
9. A car approaches a stationary police car at 36 m/s. The frequency of the siren (relative to the police car) is 500 Hz. What is the frequency (in Hz) heard by an observer in the moving car as he approaches the police car? (Assume the velocity of sound in air is 343 m/s.)
a. 220
b. 448
c. 5264
d. 552
e. 383
sound
observer
source
o
s
O
S
v vf f
v v
v
v
v
?
?
?
v
f
Doppler Shift
10. A truck moving at 36 m/s passes a police car moving at 45 m/s in the opposite direction. If the frequency of the siren relative to the police car is 500 Hz, what is the frequency heard by an observer in the truck as the police car approaches the truck? (The speed of sound in air is 343 m/s.)
a. 396
b. 636
c. 361
d. 393
e. 617
sound
observer
source
o
s
O
S
v vf f
v v
v
v
v
?
?
?
v
f
Doppler Shift
11. A truck moving at 36 m/s passes a police car moving at 45 m/s in the opposite direction. If the frequency of the siren is 500 Hz relative to the police car, what is the frequency heard by an observer in the truck after the police car passes the truck? (The speed of sound in air is 343 m/s.)
a. 361
b. 636
c. 393
d. 396
e. 383
sound
observer
source
o
s
O
S
v vf f
v v
v
v
v
?
?
?
v
f