Wave Theory for Sound Propagation

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

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:

Speed of sound ≈ 343 m/s at 20°C

Example calculation:

This is extremely important in AV acoustic design because wavelength determines:

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

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.