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

Sound in a Medium w Vibrating object displaces molecules in medium w molecules move back and forth w “bump” into others transmitting vibration thru medium

In the Medium: w We have both OSCILLATION of particles w and w TRANSMISSION of energy (or propagation)

Particle Motion w In Air, in line with transmission-- LONGITUDINAL w On Water, perpendicular to transmission-- TRANSVERSE

Displacement of Molecules in the Medium w creates areas of more molecules w --increased density--CONDENSATION w and areas of fewer molecules w --decreased density--RAREFACTION

Because We have Transmission: w We can talk about how fast sound travels in the medium = SPEED OF SOUND or c w Depends on medium, temperature, density, state w 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: w Distance Traveled during each cycle w = WAVELENGTH 8 = 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/sec wavelength = c/f = 344m/sec /86 cyc/sec = 4 m/cyc

EXAMPLE OF SOUND WAVES

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/distance 2

WHY? Surface area of sphere = 4 Pi r 2 In this case r = distance The area is proportional to distance squared

Change in Intensity = old d 2 / new d 2

EXAMPLE: w Moving from 100 m to 200 m away from source w Delta I = /200 2 w = 1 x 10 4 /4 x 10 4 = 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: w depends on size of object and wavelength of sound  when  > object’s diameter, sound passes by  when  < object’s diameter, sound blocked w 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 w closed pipes —antinode at open end and node at closed end w open pipes — antinode at each open end w closed pipe, length = ¼ l w open pipe, length = ½ l

Standing Waves in Pipes

A closed pipe only produces odd harmonics. w Frequency of harmonics = (n c)/4 L, w Where n=1, 3, 5,... w c = speed of sound w L is the length of the pipe. w In music, harmonics are called overtones.