CHAPTER 3 SOUND TRANSMISSION. Sound in a Medium w Vibrating object displaces molecules in medium w...
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Transcript of CHAPTER 3 SOUND TRANSMISSION. Sound in a Medium w Vibrating object displaces molecules in medium w...
CHAPTER 3
SOUND TRANSMISSION
Sound in a Medium
Vibrating object displaces molecules in medium
molecules move back and forth
“bump” into others transmitting vibration thru medium
In the Medium:
We have both OSCILLATION of particles and TRANSMISSION of energy (or
propagation)
Particle Motion
In Air, in line with transmission--LONGITUDINAL
On Water, perpendicular to transmission--TRANSVERSE
Displacement of Molecules in the Medium creates areas of more molecules --increased density--CONDENSATION and areas of fewer molecules --decreased density--RAREFACTION
Because We have Transmission:
We can talk about how fast sound travels in the medium
= SPEED OF SOUND or c Depends on medium, temperature, density,
state
In Air = 344 meters/sec or 1100 feet/sec
Sound Travels Out From the Source• In All Directions• (at the same speed)• So, Until Sound Encounters some object, • the “wavefront” is spherical
We Can Also Talk About:
Distance Traveled during each cycle = WAVELENGTH
λ = c/f
• Wavelength = speed of sound / frequency
Wavelength Questions:
• What is the wavelength in meters of a 1720 Hz sound traveling in air?
• What is the wavelength in meters of an 86 Hz sound traveling in air?
Question 1:
• Freq = 1720 cyc/sec, c = 344 m/sec• wavelength = c/f
• =344m/sec /1720 cyc/sec
• =0.2 m/cyc
Question 2:
• Freq = 86 cyc/sec, c = 344 m/secwavelength = c/f
= 344m/sec /86 cyc/sec
= 4 m/cyc
When Talking about Amplitude:
• Remember Power is Rate at which Work is done
(Work /Time = Power)• But the power in sound doesn’t all travel
the same direction• Only some of it reaches you.
Therefore, we are more interested in:
• How much Sound Power there is in a given area
• (e.g., the opening of ear canal, microphone)
• New term: INTENSITY = Power/Area
Remember :
• Sound Power is spread over the Wavefront• So the farther you are from the sound
source:• the larger the area over which power is
spread• the smaller the intensity
Intuitively, we all know this
• The closer you are, the louder the sound
• The farther away you are, the softer the sound
The Physics of the Situation:
• The relation between distance and intensity is an example of
• THE INVERSE SQUARE LAW
• Intensity = 1/distance2
WHY?
• Surface area of sphere = 4 Pi r2
• In this case r = distance• The area is proportional to distance squared
Change in Intensity
= old d2 / new d2
EXAMPLE:
Moving from 100 m to 200 m away from source
Delta I = 100 2/200 2
= 1 x 104/4 x 104
• = 1/4• =0.25
Decibel Notation
Intensity is measured in Watts/cm2
Range of : Just Audible 10-16 W/cm2 to to Just Painful 10-4 W/cm2
Can You Imagine?
AUDIOLOGIST: “Mr. Smith, you hearing in the right ear is down to about 3 times ten to the negative twelfth Watts per square centimeter, while your left ear is a little bit better at ten to the negative fourteenth…”
MR. SMITH: “ZZZZZZZZZZZZZ”
SO, We need a simpler set of numbers Something less unwieldy
The Solution is the BEL (after A.G. Bell)
The Genesis of the Bel
the logarithm of
the ratio of
a measurement
to a reference value
What is a log?
Log (x) = power you would raise 10 to to get x e.g., log (10) = 1 because 101 = 10 or, log (0.01) = -2 because 0.01 = 10-2
You can use a calculator to obtain logs
Inside the Logarithm is
A ratio of two numbers (or fraction)
An absolute measurement over
A reference value
The Reference Value for Intensity Level
is 1 x 10-16 Watts/cm2
Bels IL = log ( Im/ 1 x 10-16 W/cm2)
Where Im = measured intensity
The Range of Human Hearing
Detection 10-16 W/cm2 OR 0 Bels
Pain 10-4 W/cm2 OR 12 Bels
The Bel Is Too Gross a Measure For Us
So, We work in TENTHS OF BELS
The DECIBEL (dB)
dB IL = 10 log ( Im/ 1 x 10-16 W/cm2)
EXAMPLE: What is IL of sound with absolute intensity
of 2 x 10-16 W/cm2 ?
= 10 log (2 x 10-16 W/cm2/1 x 10-16 W/cm2) = 10 log (2) = 10 (0.3010) = 3 dBIL
Example--Relative Change
How will the intensity level change if you move to twice as far from a source?
We know that intensity change = old dist2 /new dist2
= 1/4 or 0.25
dB IL = 10 log (0.25) = 10 (-0.5991) = 6 dB
Bels or Decibels
Can be calculated from any measure But dB IL means something specific Another scale is dB SPL Sound Pressure Level
IMPEDANCE
The opposition to vibration, or
What, other than motion, happens to your applied force?
That is what do you have to overcome?
Impedance has 3 components:
Resistance: Energy lost to heat through friction (R)
Mass Reactance: Energy taken to overcome inertia (Xm)
Stiffness Reactance: Energy taken to overcome restoring force (Xs)
Impedance and Frequency:
Resistance is generally the same across frequency
Reactance Components change with frequency
Reactance and Frequency:
Mass reactance is greater at high frequencies --it’s harder to get massive objects to vibrate
quickly Stiffness reactance is greater at low
frequencies --it’s harder to get stiff objects to vibrate
slowly
Mass and Stiffness Reactance
0
0.2
0.4
0.6
0.8
1
1.2
100 500 1000 4000
Frequency
Rea
ctan
ce
Xm
XsRes
onan
t Fre
q.
At Resonant Frequency
Mass and Stiffness Reactance Cancel Only opposition to vibration is Resistance
In Forced Vibration, you get the most vibratory amplitude for amount of force applied
Sound Wave Phenomena
• Reflection-bouncing off an object• Absorption-sound trapped (absorbed) by
an object• Diffraction-spreading of sound into area
beyond an object• Refraction-bending of sound waves in a
medium
Sound Encountering an Object:
• Transmission-setting object into vibration• Reflection-sound bounces back• Absorption-sound becomes trapped in gaps
of surface of object
Reflected and Incident Sound Meet
• Producing INTERFERENCE
• Where the two waves meet in phase, the intensity doubles --Constructive Interference
• Where they meet out of phase, cancellation
--Destructive Interference
Getting around an Object:
depends on size of object and wavelength of sound
λ> object’s diameter, sound passes by λ< object’s diameter, sound blocked
Area of reduced or no sound energy is “sound shadow”
Diffraction
• Sound passing an object will spread to fill in area beyond it, behaving as if the edge of the object were the sound source.
Refraction
• the bending of the sound’s path produced by changes in medium
• e.g., temperature changes will bend path of sound propagation
Sound Fields
• FREE FIELD = no objects in medium
• ANECHOIC CHAMBER = room with highly absorptive walls; an attempt to create a free field.
Sound Fields (cont’d)
• SOUND TREATED ROOM = has somewhat absorptive walls, produces some reflections
• REVERBERATION ROOM = highly reflective walls set at odd angles; many reflections and complex interactions. Creates a uniform (diffuse) sound field.
Reverberation:
• Persistence of sound in a sound field after the source is turned off
• = time taken for intensity to drop to 1 millionth of initial value
• Reverberation
≈ ROOM VOL./ABSORPTION COEF.
Reverberation Time
• Least for Anechoic Chamber• Most for Reverberation Room
• Longer for larger rooms with reflective walls
Earphones
• Miniature loudspeakers to introduce sound into the ear.
• Supra-aural (sits on the pinna)• Insert (sits within external canal)• Calibrated in “artificial ears” (6cc or 2cc
couplers)
The Doppler Effect
Change in the effective frequency produced by motion of the sound source.
(or by motion of the listener)
Toward >>higher frequency Away >> lower frequency
The Doppler Effect 1
The Doppler Effect 2
Resonance• Helmholtz Resonators simulate influence of
mass and compliance (stiffness) on resonance. Tube and Cavity.
• Mass component--inversely proportional to resonant freq
• Compliance component--directly prop. to resonant freq
• Resistance -- doesn’t affect resonant freq, but produces broader tuning
Standing Waves
• Interaction between incident and reflected waves
• Produces areas of :• constructive interf. --ANTINODE• destructive interf. --NODE
Incident & Reflected Sound Meet
Incident in Black Reflected in Pink
Type of Interference varies with position.
Standing Wave Illustration
Standing Waves (cont’d)
• Intensity varies with position• Position of nodes, antinodes depends on
frequency• Distance from node to antinode is 1/4 λ• Distance from one node to the next is ½ λ
Pipes produce standing waves
closed pipes —antinode at open end and node at closed end
open pipes — antinode at each open end closed pipe, length = ¼ λ open pipe, length = ½ λ
Standing Waves in Pipes
A closed pipe only produces odd harmonics. Frequency of harmonics = (n c)/4 L, Where n=1, 3, 5, ... c = speed of sound L is the length of the pipe.
In music, harmonics are called overtones.