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Sound waves are disturbances that propagated in elastic medium, it is
also termed as a mechanical wave that results from the back and forth vibration
of particles in the medium. The sound waves consists of repetitive high-pressure
and low-pressure regions, it is also called as pressure wave. The variation of
pressure above and below atmospheric pressure due to sound waves is termed as
sound pressure measured in Pascal Pa.  A
sound instrument detect fluctuations made by the sound wave, the pressure
detection at the instrument will be as stated below.

At one instant in time, the detector
would detect a high pressure; this would correspond to the arrival of a
compression at the detector site. At the next instant in time, the detector
might detect a normal pressure. Then finally a low pressure would be detected,
corresponding to the arrival of rarefaction at the detector site. These
fluctuations as detected by the detector occurs at periodic and regular time
intervals.

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Figure
1 Soundwave with
Compression and Rarefaction

Figure
2 Output Generated after
detecting Sound Wave

The sound wave equation for pressure
filed p(r, t) is as follows

(1)

In the above equation c is the speed
of sound that can be written with thermodynamic definition of compressibility s

c =     S
=
,
(2)

Such that 0 is the density of the air. At 20o C
the speed of the sound is 331.5 m/s. The monochromatic plane sound wave can be
represented by the equation for sound pressure.

p(r, t) = Rep0
exp(i(kr – ?t)) ,                                                   (3)

In the above equation the parameters such as p0 is the maximum amplitude, ? = 2?v where v is the frequency and k is the wave
vector defined as k = (?/c)n where n
is the unit vector in direction of propagation. The time taken from t=0 to t
=1/v = T is called period. The amplitude is defined as root mean square 1.

prms
=    ,                                                   (4)

For
noise T is not the period of the wave so we calculate limit of integral as T
? ?. The sound pressure level is a logarithmic scale of level
with unit’s dB

SPL = 20 log(prms/pref) dB ,
(5)

pref is the reference pressure = 20 µ Pa.

2.1       Role of Noise
Cancellation Technology

Noise cancellation technology is a field of acoustical engineering used
for reducing unwanted ambient sound, and is implemented in different fields
such as automotive applications and large scale industries. In large scale
industries mainly in control of plane sound wave propagation in air handling
ducts, gas turbines exhausts and diesel engine exhausts noise cancellation
techniques are preferred 2. Noise reduction or
noise cancellation measures in automotive applications play significance role by
reducing the low frequency noise, so that it can increase the significant
aspects regarding safety features.

2.1.1
Importance of Noise Cancellation in Automotive Applications

The noise management in vehicle is complex, the sound produced comes
from many mechanical components. Components like multi-link suspensions, stiff
bushings and burst phase in combustion engine’s cylinders are combined and
create multiple noise paths into the cabin. In automotive applications road
noise and engine noise are two big challenges, road noise is the primary noise
distraction for the driver. The droning sound of low frequency caused by the
road noise transmitted through the vehicle structure to the car cabin increases
stress and induces driver drowsiness 3. By reducing the low
frequency noise the noise cancellation techniques will improve the safety
aspects too. The noise cancellation techniques include Active Noise
Cancellation (ANC) and Passive Noise Cancellation. The three basic principles
regarding to noise cancellation are as follows

·
Constructing a barrier between source signal and listener (Passive Noise
Cancellation).

·
Reducing the energy of a noise (Active Noise Cancellation).

·
Reducing the power of the source signal itself.

2.1.2
Passive Noise Cancellation

Passive Noise Cancellation relies on physical devices for reducing
noise, it is effectively used for reducing the noise above 1 KHz such as middle
and high frequencies. It is also termed as insulating the listener from the
external noise without using any electronics. In large scale industries the
passive noise cancellation is extensively practiced, the conventional passive
methods include sound insulation, silencers, vibration mounts and damping. In
automotive applications by using passive noise cancellation i.e. sound damping
materials leads to increase in weight of a car as a result it makes complex to
achieve emission requirements.

2.1.3
Active Noise Cancellation

Active Noise Cancellation (ANC) or Active Noise Reduction (ANR) is
actually based on coherent acoustics that accurately replicates the original
sound field. ANC relies on electronic circuits for reducing undesired noise,
ANC is achieved by creating anti-noise sound with same amplitude as reference
signal but with inverted phase. ANC is used to isolate the vehicle occupants
from low frequency road and engine noise as result it leads to improve in-cabin
experience. ANC enables automobile manufacturers to use light weight chassis
materials thereby reducing fuel consumption and emission unlike sound damping
materials in passive noise cancellation. The anti-noise generated by the ANC
algorithm will be played by using audio system of the car.

2.2       Principle

The sound
waves will interfere when pass through each other, so that the individual waves
will add together and a new wave-front is created. When the maxima of two waves
are 180o out of phase the positive displacement of one wave is cancelled exactly
by a negative displacement of the other wave. Such that the resultant amplitude
is zero, this phenomenon is called destructive interference.