Reflection, refraction, diffraction Sound Propagation Reflection, refraction, diffraction

What do we know about sound propagation? Speed of sound in air Speed of sound in solids/liquids/gases Sequences of compression and rarefaction (click me)

Classification Infra sound 20 Hertz Audible range 20 000 Hertz=20kHz Earthquakes, heavy traffic 20 Hertz 3000 Hz best hearing Audible range 20 000 Hertz=20kHz Ultra sound Medical imaging, dog whistles, bats Growing Wave length? Growing frequency

Wave lengths of the audible range 20 kHz: 20 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 space? Direction of propagation Rays Surfaces of equal compression = planes Wave fronts Plane waves

How can we represent sound in space? How many rays are there? Direction of propagation Where do you measure the wavelength? Surfaces of equal compression = spheres Rays Spherical waves

Comparison Plane waves spherical waves Parallel rays Radial 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 surface Will all these rays be reflected back to the person? Can the blue person hear the echo? Reflection

Waves encountering a surface Specular Reflection

Waves encountering a surface Diffuse Reflection

How can the two people hear each other? Each of the rays traveled different lengths of way Each of the rays used a different amount of time

Variable speed of sound Rays are bent away From surface! Cool air = low speed Refraction Wave front Plane waves at constant speed Warm air = high speed Wave fronts if the air is warmer at the ground

Variable speed of sound Rays are bent toward surface! Warm air = high speed inversion Refraction Wave fronts if the air is cooler at the ground Cool air = low speed

Variable speed of sound wind sound Resulting motion of sound waves The rays are bent upward upwind of the source. The rays are bent downward downwind of the source. Refraction

Reflection and refraction At solid obstacles, a sharp change of direction Echo, ringing effect in halls Refraction: Inhomogeneous speed, gradual change of direction Air layers with different temperatures, wind Reflection is of more importance to us than refraction.

Why can we hear around a corner? Reflection ?

Sound waves at obstacles Top view: Diffraction

Diffraction at small opening Small: d<<λ Wavelength large compared to opening Diffraction bends the wave fronts heavily at the edges of a small Obstacle. Shadow zone Shadow zone

Diffraction at large opening Small: d>>λ Wavelength small compared to opening Shadow zone Diffraction bends the wave fronts only lightly at the edges of a large obstacle. Shadow zone

Where can we observe diffraction? Speak to a person, but not directly: Mouth: 5 cm<< wave length 10..30 cm Speakers: Bass sounds spread in all directions Treble more clearly in a narrow cone Your left ear hears sound coming from right: Bass more clearly Treble not that clearly

Outdoor Music Problems: Waves propagate away from source (no wall reflections) Deadness (no overlap from secondary reflections) Uneven distribution over a large audience

Possible solutions “Shell” behind the performers Audience

Possible Solutions Shell behind performers: top view Ideal position for performer: a little closer than half the radius of curvature

Possible Solutions Roofed outdoor pavilions: Traps sound Not good for outside audience

Possible Solutions Roofed outdoor pavilions: Helps audience Band members can hardly hear each other

Possible Solutions Roofed outdoor pavilions: compromise Okay for band and audience