Wang X. Vehicle Noise and Vibration Refinement

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Vehicle interior noise reﬁ nement – cabin sound package design 295

where:

β is the angle of incidence of the sound wave over the surface of the given

panel

λ is the wavelength of the acoustic wave in air

is the wavelength of the bending wave in the structure.

The frequency at which this occurs is called the ‘coincidence frequency’.

It is easy to see from Equation 13.7 that if the wavelength of the sound

in air is greater than the wavelength of the bending waves in the structure

there are no wave coincidence phenomena. Usually at low frequencies λ is

much greater than λ

. Furthermore, as frequency increases, λ decreases

more quickly than λ

(see Fig. 13.6), so there is always a frequency where

the two wavelengths are the same: the ‘critical frequency’ f

is deﬁ ned as

the minimum frequency at which a wave coincidence may occur, so it is the

minimum possible value for the coincidence frequency. From Equation 13.7

it can be seen also that over the critical frequency there is always a given

angle of incidence β at which the wave coincidence phenomenon may occur.

It can be shown (Beranek, 1960) that:

18.sin

(13.8)

where:

is the speed of longitudinal waves in the plate

h is the thickness of the plate structure.

In the panels of a common car this frequency is usually very high (often

above the frequency range of interest), but for very thick panels and for all

1.00

10.00

100.00

1000.00

10000.00

100000.00

0 2000 4000 6000 8000

1200010000

Frequency (Hz)

Wavelength (mm)

13.6 Coincidence frequency.

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296 Vehicle noise and vibration reﬁ nement

the glass of the car it falls within an important frequency range (i.e.

3000–5000 Hz).

13.4.2 Sound absorption

Sound absorption is a very well-known and commonly used solution to

reduce noise. It exploits the characteristics of some materials that are able

to dissipate the acoustic energy. In current vehicles sound absorbing materi-

als are applied in the passenger cabin and often in the engine bay, to reduce

the interior and sometimes the exterior noise.

There are three main physical phenomena related to sound absorption.

The ﬁ rst mechanism is the frictional losses of the air molecules; a sound

wave causes an oscillation in the position of the air particles: the molecules

of the air interact with the pores or the ﬁ bres of the absorbing materials

and are subjected to friction phenomena, causing a loss of energy (the fric-

tion slightly increases the temperature of the air and the material). A

second mechanism is related to heat exchange; the sound wave generates

pressure ﬂ uctuations in the air; in the free ﬁ eld this is an adiabatic trans-

formation, whereas on the boundaries the presence of absorbing materials

(with a large surface to volume ratio) causes a heat exchange between the

air and the surrounding materials. The transformation is no longer adia-

batic and shifts towards an isothermal transformation, causing a loss of

energy in the sound wave. This could happen mainly at low frequencies,

where there is more time during a cycle for heat exchange (at high fre-

quency the heat exchange becomes so small that it can be neglected). The

third mechanism is related to the internal losses of the acoustic materials

subjected to the forced mechanical oscillations caused by the acoustic pres-

sure: this is true mainly for closed-cell porous materials, whereas in ﬁ brous

and open-cell porous materials this effect is so low that it can generally be

neglected.

The most important characteristics of the sound absorbing materials are

listed below.

Normal speciﬁ c acoustic impedance

At the boundary between the air and a denser medium like an absorbing

material the air particles are moving in the presence of an acoustic wave:

their velocity u is an alternate velocity in a given direction through the

material’s surface. The direction depends on the angle of incidence of the

acoustic wave and on the properties of the absorbing material. A ﬁ rst

important deﬁ nition for the properties of an acoustic material is the ‘normal

speciﬁ c acoustic impedance’ (Z

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Vehicle interior noise reﬁ nement – cabin sound package design 297

(13.9)

where:

p is the sound pressure on the boundary between the air and the mate-

rial’s surface

is the normal component of the particle’s velocity at the material’s

surface.

is a complex value and is an important property that describes the

behaviour of an absorbing material in the presence of normal incident

sound waves.

Energy absorption coefﬁ cient

The most important deﬁ nition for the characterisation of an acoustic mate-

rial is the ‘energy absorption coefﬁ cient’ (α), which is deﬁ ned as the ratio

between the absorbed acoustic energy and the total incident acoustic

energy. In all the reﬂ ections of acoustic waves on a surface the energy is

partially reﬂ ected and partially absorbed by the material, and this coefﬁ -

cient represents the capability of the material to absorb the acoustic energy.

The value α = 1 means that all the energy is absorbed, so there are no

reﬂ ected waves by the surface; a value α = 0 means that there is perfect

reﬂ ection, without any loss of energy.

The coefﬁ cient α depends on the material properties and the thicknesses

of all the layers applied on the surface (absorbing materials, air gaps, etc.).

Also, α is usually a function of the frequency and the angle of incidence of

the sound wave, as in the case of the TL. For this latter reason it is common

to deﬁ ne an absorption coefﬁ cient for a diffuse ﬁ eld (α

), where the angle

of incidence covers all the angles between 0° and 90°.

Closed rooms, reverberation time, Eyring and Sabine theory

For a given closed room (like a vehicle cabin) it is possible to deﬁ ne an

‘average diffuse ﬁ eld sound absorption’ (

) (Beranek, 1960):

∑

(13.10)

where:

i is the number of surfaces closing the room

is the diffuse ﬁ eld absorption coefﬁ cient for the ith surface

is the area of the ith surface.

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298 Vehicle noise and vibration reﬁ nement

The sound absorption of a closed room can be measured by its ‘rever-

beration time’ (T

), deﬁ ned as the time required (in seconds) to reduce the

noise by 60 dB after turning off the acoustic sources inside the room. There

are many diffuse ﬁ eld models, the most interesting for vehicle applications

being the Sabine theory. In order to better understand the Sabine formulas

it is possible to start with the most generally applicable diffuse ﬁ eld model,

the Eyring theory, applicable for a point source:

Lr L

() log=+ +

(

)

(13.11)

valid for steady-state conditions, where:

is the sound pressure level

is the sound power level of the source

Q is the directivity factor for the point source (the ratio of the sound

power radiated in the receiver direction to the mean sound power

radiated in all directions; equal to 1 for a homogeneous sound source)

r is the distance between the point source and the receiver

R is the so-called room constant, given by:

mV S

−⋅ −

−

ln( )

(13.12)

where:

2m is the energy air absorption exponent (Beranek, 1960)

V is the room volume

S is the whole surface of the room.

Equation 13.11 describes the sound ﬁ eld in a room as the summation of a

direct and a reverberant component (the two terms in the parentheses).

Also, the Eyring theory states that the reverberation time is given by (in

SI units):

cmVS

55 3

−⋅ −

[]

ln( )

(13.13)

where c is the speed of sound in air.

In practical vehicle applications the average diffuse ﬁ eld sound absorp-

tion coefﬁ cient is usually quite small (<0.25); in this case it is better to use

the Sabine theory. Also, the air absorption can be neglected, that is

2m = 0 (it is only important for propagation distances greater than about

10 m). In this case Equations 13.12 and 13.13 become:

−

(13.14)

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Vehicle interior noise reﬁ nement – cabin sound package design 299

55 3

(13.15)

Equations 13.11 and 13.14 show that the direct ﬁ eld (dominating near the

source) decreases by 6 dB when doubling the distance from the source,

whereas the reverberant ﬁ eld (dominating far from the source) depends

only on the absorption of the room, and is about inversely proportional to

and S (for small values of

). Equation 13.15 shows that the reverbera-

tion time is directly proportional to V/

S. These equations allow for meas-

uring an absorption coefﬁ cient by measuring the reverberation time. The

term

S is also called the ‘total room absorption’ or ‘equivalent area of

absorption of the room’ and represents the equivalent area with absorption

coefﬁ cient equal to 1.

It is important to know that for normal incidence acoustic waves it is

sufﬁ cient to measure the normal impedance of the material without meas-

uring the diffuse ﬁ eld absorption coefﬁ cient.

13.4.3 Measuring facilities

There are different testing facilities and procedures for measurement of the

acoustic properties of the acoustic package. The most interesting for vehicle

applications are described below.

Anechoic and semi-anechoic rooms

Anechoic rooms are closed rooms with all the walls (including ﬂ oor and

ceiling) covered by strong absorbing materials, usually cones made of

mineral or glass ﬁ bres. An ideal anechoic room should have a unit absorp-

tion coefﬁ cient in all the walls, in order to have a free-ﬁ eld radiation condi-

tion inside the room. Obviously this is not completely feasible, mainly at

low frequencies where it is really hard to achieve a high level of absorption.

For this reason an anechoic room has a minimum working frequency

(usually 100–200 Hz) and measurements inside the room can be made only

at higher frequencies.

In order to allow work inside an anechoic room (where also the ﬂ oor is

covered by acoustic treatments) it is usual to build a suspended ﬂ oor made

of metal wires with a small reﬂ ecting surface. Semi-anechoic rooms are the

same as anechoic rooms except that the ﬂ oor is a reﬂ ecting surface: in this

way it is possible to reproduce a free-ﬁ eld radiation in the presence of a

reﬂ ective ground, like the road for vehicles.

Reverberant rooms

Reverberant rooms are the opposite of anechoic rooms, as the goal is to

reproduce a reverberant and diffuse ﬁ eld inside them. For this reason all

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300 Vehicle noise and vibration reﬁ nement

the walls, including ﬂ oor and ceiling, have to perfectly reﬂ ect the sound

waves. Furthermore, to avoid cavity resonance phenomena it is usual to

build non-parallel walls (including the ceiling), and sometimes to add

reﬂ ecting and non-planar shields in random positions to reﬂ ect and diffuse

the waves in all possible directions, to generate a ﬁ eld with waves travelling

with all the angles of incidence (diffuse ﬁ eld). In the low-frequency range

the cavity resonance phenomena are still important, so there is a transition

frequency above which the ﬁ eld can be described in statistical terms. The

sound ﬁ eld obtained is still not perfectly uniform and diffuse, so it is neces-

sary to take some spatial averages of the sound pressure in order to have

reliable measurements.

Reverberant rooms are used to measure the absorption of a given mate-

rial or component by exploiting the Sabine formula (Equation 13.15); by

measuring the reverberation time with and without the component it is

possible to ﬁ nd its absorption coefﬁ cient. This measurement is deﬁ ned by

the international standard procedure ISO 354-1985 and requires a rever-

beration room of at least 294 m

Alpha cabin

In the automotive ﬁ eld it has become a common standard to use reverbera-

tion rooms (known as alpha cabins) that are smaller than the standard ISO

requirements for measurement of the acoustic absorption of the materials.

The basic principle of measurement is the same.

Kundt’s tube

Measurement of the normal impedance and the absorption coefﬁ cient for

normal incidence waves can be done in the laboratory with a smaller facility

than a reverberant room. This is the impedance tube or Kundt’s tube (see

Fig. 13.7), and the international standard procedures for the measurement

are ASTM-E 1050 and DIN 52215. A disc of the test material is placed in

the side opposite to the acoustic source (loudspeaker) and the acoustic

normal impedance is calculated by the sound pressure levels measured by

the microphones inside the tube.

Transmission loss measurement

The measurement of the TL of a given partition is deﬁ ned by international

standard procedures, in particular ISO 140/3–1995 and ASTM E90-74.

They require the use of two reverberant rooms (with a volume of at least

64 m

) both facing the same window where the test partition can be placed

(see Fig. 13.8). The window (and consequently the partition) has dimen-

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Vehicle interior noise reﬁ nement – cabin sound package design 301

sions of 2.8 by 3.6 m. The ﬁ rst room is used for the source, using one or

more loudspeakers covering the whole frequency range of interest and

generating a diffuse ﬁ eld. In the second room the noise attenuated by the

test partition is measured: it is very important to have only the acoustic

path that comes through the test partition, avoiding any leakages and with

very good isolation of the common wall between the two reverberant

rooms.

Acoustic source

(speaker)

Absorbing material

Mic.1

Mic.2

13.7 Kundt’s tube.

out

Microphone

13.8 Transmission loss measurement.

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302 Vehicle noise and vibration reﬁ nement

The measurement procedure follows three steps:

1. Measurement of the incident acoustic ﬁ eld

2. Measurement of the transmitted acoustic power through the partition

3. Measurement of the total absorption area of the receiver room.

Equation 13.2 requires the measurement of the incident and transmitted

sound power. If we consider an incident diffuse ﬁ eld, the incident sound

power will be:

WIS

in in p

in p

(13.16)

where:

is the sound intensity in the source room

is the area of the test partition

> is the time and space averaged mean-square sound pressure in the

source room (it should be constant in a real diffuse ﬁ eld, but consider-

ing that a reverberant room cannot give an exact diffuse ﬁ eld this

pressure has to be averaged with spatial sampling).

The measurement of the transmitted power through the partition can be

obtained by a power balance in the receiver room:

out

out rec

(13.17)

where:

out

> is the time and space averaged mean-square sound pressure in the

receiver room

rec

is the equivalent absorption area of the receiver room.

Equation 13.2 then gives (for a diffuse incident ﬁ eld):

out

in p

out rec

out

=− +

10 10

log log

log

(13.18)

where:

is the time and space averaged sound pressure level in the source

room

out

is the time and space averaged sound pressure level in the receiver

room.

The measurement of the TL of vehicle components commonly uses

slightly smaller rooms (with some restrictions in the frequency range).

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Vehicle interior noise reﬁ nement – cabin sound package design 303

Often, the receiver room used is an anechoic room: Equation 13.18 shows

that it is still possible to measure the TL, just by measuring the total equiva-

lent absorption area of the receiver room. The advantage is that with such

a facility it is also possible to make sound intensity measurements in the

receiver room in the near ﬁ eld of the test partition, obtaining acoustic maps

that qualitatively show the areas of the partition with the high level of

transmission.

13.4.4 Acoustic material characteristics

There are some physical properties that make certain materials suitable for

use as acoustic treatments (Beranek and Ver, 1992). The ﬁ rst important

property is the resistance that the material offers to an airﬂ ow through it

(as described in Section 13.4.2, one of the mechanisms of acoustic energy

absorption is the friction of the air and the ﬁ bres or the pores of the

material). One of the most important quantities is then the ‘speciﬁ c ﬂ ow

resistance’ (σ):

Δp

(13.19)

where:

Δp is the pressure difference between the two sides of the material

specimen

u is the mean air particle velocity through the specimen

d is the thickness of the specimen crossed by the airﬂ ow.

A second important property is the density of the material and its ‘porosity’

(Φ):

Φ=

(13.20)

where:

is the volume of the air included in the material

is the total volume of the material, including the air inside it.

The ﬂ ow resistance is related to the porosity, the ﬁ bre diameter and the

so-called ‘structure factor’ or ‘tortuosity’, which depends on tortuous paths

that the air has to follow crossing the material: it takes into account the

effect of openings that are perpendicular to the propagation direction of

the sound wave.

Another parameter, important only for materials with a consistent struc-

ture, is the ‘volume coefﬁ cient of elasticity of the skeleton’ (Q), which

measures the compression stiffness of the material: it is measured using a

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304 Vehicle noise and vibration reﬁ nement

ﬂ at layer of material (with a thickness d) compressed with a force (F) that

acts uniformly on the entire surface of the material (of area S). The mea-

surement of the thickness reduction (Δd) gives the coefﬁ cient Q:

(13.21)

Another property of materials for noise control applications is the ‘loss

factor’ (η), which is important for the reduction of the structure vibrations.

It comes from the measurement of the complex Young modulus (E) of the

material subjected to a dynamic load:

E = E′ + iE″ (13.22)

′′

′

tan

(13.23)

where:

E′ is the ‘storage modulus’ (real part of the complex Young modulus)

E″ is the ‘loss modulus’ (imaginary part of the complex Young modulus)

δ is the phase angle.

The most common materials used on vehicle applications are described

below.

Porous materials

All materials with a given porosity on their surface have some sound-

absorbing properties. Usually the materials used are open-cell foams

(i.e. polyurethane); closed-cell foams are not very useful for acoustics appli-

cations, as they work only on their surface and do not allow air to ﬂ ow

through them (the ﬂ ow resistivity is very high). The common open cells

used in acoustics have pores smaller than 1 mm, so they are much smaller

than the wavelength. In many porous materials the continuous solid struc-

ture behaves also as an elastic structure, adding stiffness and damping to

the panels of the structures: in this case they are called poroelastic

materials.

Fibrous materials

Fibrous materials are very common in sound absorbing isolation as they

may be optimised to have the required speciﬁ c ﬂ ow resistance, porosity and

tortuosity, by changing the diameter of the ﬁ bres and their geometrical

orientation. Fibrous materials are in general based on mineral, glass or

natural ﬁ bres.

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