Sound field descriptors

Eng.Ivaylo Hristev

Contents

1. Wave acoustics. Room resonances.

2. Ray acoustics. Raytracing.

3.Statistical acoustics. Reverberation time.

Schroeder frequency

Division of the audible range. Source: Davis&Davis, 1987

1.Wave acoustics. Wave equation.2

22 2

2 2 2 2

2 2 2 2 2

10;

10.

ppc t

p p p p

x y z c t

3 dimensional wave equation

General solution

Private solution

Private solution with eigenfunctions in 3D

For rectangular rooms with hard walls, the private solutions are described as modes ( standing waves ) and are described with the following formula:

•nx , ny and nz are whole number parameters;•lx , ly and lz are the room dimensions.•Each three parameters represent room resonance.

222

2

z

z

y

y

x

x

l

n

l

n

l

ncf

Standing waves – room modes

Sound pressure distribution in a room for axial mode (0,2,0)

Standing waves – room modes

Sound pressure distribution in a room for tangential mode (1,1,0)

Wave propagation Pressure distribution

Standing waves – room modes

Sound pressure distribution in a room with tangential mode (2,1,0)

Standing waves – room modes

mode (1,0,0)

mode (1,1,0)

mode (?,?,0)

Standing waves – room modes

mode (1,0,0)

mode (1,1,0)

mode (3,2,0)

Standing waves – room modes

Room modes in 3 dimensions

Axial modes(nx,0,0)(0,ny,0)(0,0,nz)

Tangential modes(nx, ny,0)(nx, 0,nz)(0, ny, nz)

Oblique modes(nx, ny, nz)

Real life measurements

Real life measurements

Different mode types have different energy and decay in a different way. Tangential modes have ½ of the energy of the axial modes; oblique modes have ¼ of the energy of the axial modes.

Room mode excitation

Non rectangular room modes

2.Ray acoustics.

This method makes use of an approximation of the sound wave with a ray. This is analogous to the light rays. By doing so it is straightforward to trace the path of the wave using Snell’s law.

Source: http://www.cs.princeton.edu/~funk/acoustics.html

Raytracing algorithms

3. Statistical acoustics

This method uses only statistical properties of sound field in a room. It is assumed that the sound field is diffuse; this is not true in every room, but results from the theory are within reasonable practical limits.

Reverberation

Reverberation time

Reverberation time can be calculated by the well known Sabine formula:

Т60 is the time it takes for the sound energy to decay 1000000 times, or sound pressure level decrease of 60 dВ. After this time the sound is considered inaudible.

A

VT 163,060

The total sound absorption А is the sum of the product of the sound absorption coefficient by the area of each surface in the room. It is called metric Sabines.

А is the sum of the sound absorption of any additional objects, such as people or furniture.

ASА ii

The modified formula is known as Eyring formula, gives better results in rooms with large absorption:

1ln163,0

общоS

VT

When calculating Rt for big rooms, the air absorption must be accounted for:

Here m is the air absorption coefficient.

mVS

VT

41ln161,0

Sound absorption of air

Measuring Rt requires the generation of sound field within the room of interest. The stimulus is then interrupted and the sound decay process is recorded. Usually the measurement stimulus is a special type of noise, and the analysis is done in 1/3 octave bands. The recorded sound should be at least 20 dB above noise. This is rarely possible, that’s why usually the measurements are done by following the decay rate for 10dB (T10), 20 dB (T20) or 30 dB (Т30) and the result is extrapolated to 60 dB.

Reverberation time measurements

Reverberation time measurements

500Hz 1000Hz

2000Hz

EDT, T30

Reverberation time measurements

Averaged reverberation time as function of frequency

Critical radiusClose to the sound source, the sound pressure drops by 6 dB for distance double. In rooms, the zone for which this holds is within the so called critical radius, at which the direct sound and reverberant field equalize. Beyond this distance – the reverberant field dominates:

Here В is the room constant calculated by:

50

Brcr

average

totalАB

1