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Wave Theory for Sound Propagation
Wave theory explains that sound propagates through a medium as longitudinal pressure waves created by alternating compressions and rarefactions of particles.
Basic Principle
Wave theory of sound propagation explains that sound travels through a medium (air, water, or solids) as a mechanical longitudinal wave.
Instead of the sound source moving through space, energy travels by vibration of particles in the medium.
When a sound source vibrates (like a loudspeaker diaphragm):
-
It pushes nearby air molecules together → Compression
-
Then molecules spread apart → Rarefaction
-
This repeating process creates a pressure wave that travels outward.
So, the air molecules oscillate back and forth, but the wave energy moves forward.
Key Elements of Sound Waves
Compression
-
Region where air molecules are close together
-
High pressure region
Rarefaction
-
Region where molecules are spread apart
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Low pressure region
Wavelength (λ)
Distance between two consecutive compressions or rarefactions.
Frequency (f)
Number of wave cycles per second.
-
Measured in Hertz (Hz)
-
Determines pitch
Amplitude
Height of the wave.
-
Determines loudness
-
Related to sound pressure level (SPL)
Wave Speed Relationship
Sound propagation follows a fundamental relation:
v=fλ
Where:
-
v = speed of sound
-
f = frequency
-
λ = wavelength
Example in air:
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Speed of sound ≈ 343 m/s at 20°C
Example calculation:
| Frequency | Wavelength |
|---|---|
| 100 Hz | 3.43 m |
| 1 kHz | 0.343 m |
| 10 kHz | 0.034 m |
This is extremely important in AV acoustic design because wavelength determines:
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Speaker spacing
-
Phase interaction
-
Room modes
-
Acoustic treatment thickness
Types of Sound Waves
Longitudinal Waves
Sound propagates parallel to particle motion.
Example:
-
Air sound waves
-
Loudspeaker output
Spherical Waves
-
From a point source sound spreads in all directions.
-
Used in room acoustic modeling.
Plane Waves

-
Sound propagates in a single direction with flat wavefronts.
-
Used in waveguide and line array theory.
Sound Propagation in Different Mediums
| Medium | Speed of Sound |
|---|---|
| Air | 343 m/s |
| Water | 1480 m/s |
| Steel | 5960 m/s |
Reason: particle density and elasticity.
Wave Behaviors in Rooms (Important for AV Engineers)
When sound propagates in rooms, waves interact with surfaces.
Reflection
Sound bounces from surfaces.
Used in:
-
concert hall design
-
room acoustics
Diffraction
Sound bends around objects.
Important for:
-
speaker placement
-
coverage prediction
Absorption
Materials convert sound energy to heat.
Used in:
-
acoustic panels
-
bass traps
Interference
Two waves combine.
Results:
-
constructive interference
-
destructive interference
Critical in:
-
line array tuning
-
multi-speaker systems
Practical Example (AV System Design)
In sound system design (EASE / AV modeling) wave theory helps determine:
-
speaker spacing
-
phase alignment
-
delay settings
-
room mode frequencies
-
coverage prediction
-
acoustic treatment thickness
Example:
Low frequency 100 Hz, Wavelength ≈ 3.4 m
So acoustic treatment must be ~0.8–1 m thick to fully absorb it.
Sound propagation = Energy traveling through particle vibrations forming pressure waves in a medium.
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