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.