1. Reflection, refraction, diffraction
Sound Propagation
Reflection, refraction, diffraction

2. 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)

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

4. 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.

5. How can we represent sound in space?
Direction of
propagation
Rays
Surfaces of equal compression = planes
Wave fronts
Plane waves

6. 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

7. 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 …

8. Waves encountering a surface
Will all these rays
be reflected
back to the person?
Can the blue person hear
the echo?
Reflection

9. Waves encountering a surface
Specular
Reflection

10. Waves encountering a surface
Diffuse
Reflection

11. 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

12. 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

13. 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

14. 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

15. 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.

16. Why can we hear around a corner?
Reflection ?

17. Sound waves at obstacles
Top view:
Diffraction

18. 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

19. 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

20. Where can we observe diffraction?
Speak to a person, but not directly:
Mouth: 5 cm<< wave length 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

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

22. Possible solutions
“Shell” behind the performers
Audience

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

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

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

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