ACOUSTICS

Sound in a Medium Sound Wave Phenomena Sound Fields Earphones Resonance and Standing Waves

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

= 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

EXAMPLE OF SOUND WAVES

http://rustam.uwp.edu/GWWM/sound_waves.html

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

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

when > object’s diameter, sound passes by

when < 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.

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)

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

Standing Wave Illustration

Standing Waves (cont’d)

• Intensity varies with position• Position of nodes, antinodes depends on

frequency

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 l open pipe, length = ½ l

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.