Sound PropagationSound Propagation

Reflection, refraction, Reflection, refraction, diffractiondiffraction

What do we know about sound What do we know about sound propagation?propagation?

Speed of sound in airSpeed of sound in air

Speed of sound in Speed of sound in solids/liquids/gasessolids/liquids/gases

343 / 0.6*( 20) /v m s T m s Sequences Sequences

of compressionof compression

and rarefactionand rarefaction

((click me)

v f

ClassificationClassification

Growing frequency

20 Hertz

20 000 Hertz=20kHz

Audible range3000 Hz best hearing

Infra sound

Ultra sound

Growing Wave length?

Earthquakes, heavy traffic

Medical imaging, dog whistles, bats

Wave lengths of the audible rangeWave lengths of the audible range

20 kHz: 20 kHz:

20 Hz: 20 Hz:

20000 340 /

340 /0.017 1.7

20000

v f Hz m s

m sm cm

Hz

20 340 /

340 /17

20

v f Hz m s

m sm

Hz

Width of a finger

Width of a house

Objects in our environment are of the same order of size as the wave length of sound waves.

How can we represent sound in How can we represent sound in space?space?

Surfaces of equal compression = planes

Direction ofpropagation

Wave fronts

Rays

Plane waves

How can we represent sound in How can we represent sound in space?space?

Direction ofpropagation

RaysSurfaces of equal compression = spheres

Spherical waves

How many raysare there?

Where do you measure the wavelength?

ComparisonComparison Plane wavesPlane waves spherical wavesspherical waves

Parallel raysRadial rays

Wave fronts are planes Wave fronts are spheres

Amplitude is constant Amplitude diminishes with distance from source

Rays are perpendicular to wave fronts

Rays straight lines, except …

Waves encountering a surfaceWaves encountering a surface

Will all these raysbe reflected back to the person?

Can the blue person hearthe echo?

Reflection

Waves encountering a surfaceWaves encountering a surface

SpecularReflection

Waves encountering a surfaceWaves encountering a surface

DiffuseReflection

How can the two people hear each How can the two people hear each other?other?

Each of the rays traveled different lengths of way

Each of the rays used a different amount of time

Variable speed of soundVariable speed of sound

Cool air = low speed

Warm air = high speed

Wave front

Plane waves at constant speed

Rays are bent away From surface!

Refraction

Wave fronts if the air is warmer at the ground

Variable speed of soundVariable speed of sound

Cool air = low speed

Warm air = high speed

inversion

Rays are bent toward surface!

Wave fronts if the air is cooler at the ground

Refraction

Variable speed of soundVariable speed of sound

wind

sound

Resulting motionof sound waves

Resulting motionof sound waves

sound

wind

The rays are bent upward upwind of

the source.

The rays are bent downward downwind of

the source.

Refraction

Reflection and refractionReflection and refraction

Reflection:Reflection:– At solid obstacles, a sharp change of At solid obstacles, a sharp change of

direction direction – Echo, ringing effect in hallsEcho, ringing effect in halls

Refraction:Refraction:– Inhomogeneous speed, gradual change Inhomogeneous speed, gradual change

of directionof direction– Air layers with different temperatures, Air layers with different temperatures,

windwindReflection is of more importance to us than refraction.

Why can we hear around a corner?Why can we hear around a corner?

Reflection ?

Sound waves at obstaclesSound waves at obstacles

Top view:

Diffraction

Diffraction at small openingDiffraction at small opening

Small: d<<λWavelength large compared to opening

Shadow zone

Shadow zone

Diffraction bends the wave fronts heavily at the edges of a smallObstacle.

Diffraction at large openingDiffraction at large opening

Small: d>>λWavelength small compared to opening

Shadow zone

Shadow zone

Diffraction bends the wave fronts only lightly at the edges of a largeobstacle.

Where can we observe diffraction?Where can we observe diffraction?

Speak to a person, but not directly:Speak to a person, but not directly:– Mouth: 5 cm<< wave length 10..30 cmMouth: 5 cm<< wave length 10..30 cm

Speakers:Speakers:– Bass sounds spread in all directionsBass sounds spread in all directions– Treble more clearly in a narrow coneTreble more clearly in a narrow cone

Your left ear hears sound coming Your left ear hears sound coming from right:from right:– Bass more clearlyBass more clearly– Treble not that clearlyTreble not that clearly

Outdoor MusicOutdoor Music

Problems:Problems:– Waves propagate away from source (no Waves propagate away from source (no

wall reflections)wall reflections)– Deadness (no overlap from secondary Deadness (no overlap from secondary

reflections)reflections)– Uneven distribution over a large Uneven distribution over a large

audienceaudience

Possible solutionsPossible solutions

““Shell” behind the performersShell” behind the performers

Audience

Possible SolutionsPossible Solutions

Shell behind performers: top viewShell behind performers: top view

Ideal position for performer: a little closer than half the radius of curvature

Possible SolutionsPossible Solutions

Roofed outdoor pavilions:Roofed outdoor pavilions:

Traps sound

Not good for outside audience

Possible SolutionsPossible Solutions

Roofed outdoor pavilions:Roofed outdoor pavilions:

Helps audience

Band members can hardly hear each other

Possible SolutionsPossible Solutions

Roofed outdoor pavilions:Roofed outdoor pavilions:

compromise

Okay for band and audience