Residential areas face major issues if loud noise producing engines or machines are placed in nearby. Equipment with IC engines produces loud noise in exhaust. It has been well-known that for humans, the noise level should be below 80 dB (decibels). Therefore, component called muffler is used for attenuation of noise. Any device used for noise reduction, has number of parameters which defines the effectiveness. Therefore, the design of the muffler plays an important role as it affects the noise cancellation^{4}. A series of experiments suggest that the length of expansion chamber should be between 1.2 to 1.7 times of diameter of chamber

There are very limited studies focusing on extended inlet muffler. Therefore, the research focus on diameter of inlet extension will lead more detailed design methodology. Muffler is noise reducing assembly. Experimental results are measured using microphones. For theoretical understanding, using real life conditions variables are formed which are implemented in various equations to develop a mathematical model of noise reduction. The number of variables are high and with large number of elements, it becomes more complicated and time consuming to find accurate values. Computer program MATLAB provides significant support in such calculations. These results are then compared with FEA and real-life experiments.

Transmission Loss (TL) is calculated according to the empirical formula given below for theoretical analysis of single expansion chamber reactive muffler.

Where,

m = Expansion ratio = cross-sectional area of expansion chamber to cross-sectional area of inlet & outlet pipe.

k = Wave number =

c = Velocity of sound (in m/s)

l = Length of expansion chamber (in m)

TL = Transmission Loss; dB

In theoretical analysis, various design parameter used for basic model of muffler are indexed below and Transmission Loss is evaluated.

a. The length of expansion chamber is kept constant i.e., L = 535 mm.

b. The diameter of expansion chamber is kept constant i.e., D = 120 mm.

c. The diameter of inlet and outlet pipe connected to expansion chamber is kept constant i.e., d = 40mm.

d. The length of inlet pipe and outlet pipe connected to expansion chamber is kept constant i.e., l_{1}_{ }= 90 mm and l_{2}_{ }= 90 mm

e. The length of Extended inlet = 240 mm

f. The diameter of extended inlet is varied from 10 mm to 50 mm with step size of 10 mm.

The MATLAB script is prepared, and for the purpose of analysis the frequency range is set from 1 to 1600 Hz.

A 3D muffler model in form of CAD was drafted for simulation. The ^{ }

Well-known acoustic Helmholtz empirical equation is used to estimate sound pressure P,

Where,

Where,

The inlet pressure value

The model uses sound hard wall boundary conditions at the solid boundaries as by following equation,

The numerical analysis is carried out for the frequency range of 1-1600 Hz. the results are shown in the form of graph in

The

Further, verification of the analytical model with outstanding acoustics performance is carried out using the Two Load approach in the experiment analysis.

Using the transfer matrix approach, one may simply determine the transmission loss of any muffler by solving four pole equations from the four microphone positions^{ }

The acoustic output of a muffler can be analyzed through equations, based on above four microphone positions to calculate transmission loss. The four poles for elements 1-2 can be stated as

The equation (7) states four poles for elements 2-3 as

Where,

The equation (8) describes four poles for elements 3-4 as

The transfer function between

The final Transfer matrix is stated as follows

The Transmission Loss is given by

The equation (10) is used for calculating experimental Transmission Loss.

^{ }

Muffler is attached with 4 microphones, 2 on inlet tube while 2 on outlet tube. The various studies done in past have also followed same setup and method of experimentation to observe the results.

The troughs are obtained at 641 Hz and 1281 Hz - the points of local minimum. The muffler model showing uplifted troughs is considered as good model. The crests are observed at 321 Hz, 941 Hz and 1581 Hz - the crest means point of local maximum. The maximum transmission loss indicates that, minimum noise is radiated at the specified frequency. The experimental results and FEM results shows good agreement. The small difference in the experimental outcome from that of the FEM result is attributable to sound leakage from the impedance tube, FFT white noise production issues, impedance tube imprecise surface finish consistency^{ }

In this research paper, acoustic analysis of extended inlet with variation in diameter in the single expansion chamber reactive muffler is analysed using different methodologies Viz Numerical analysis and Experimental analysis. The COMSOL Multiphysics is used for modelling, meshing and finite element analysis. The frequency domain is used for the analysis. In the Experimental analysis, Two Load method is used. Loads are varied without making change in position of source. It is observed that, with increase in extended inlet diameter, the average Transmission Loss increases up to 20 mm by 28%. Although, TL reduces for 30 mm and for 40 mm while increases for 50 mm. Therefore, comparatively, an effective value of 20 mm is the best suitable for this configuration. The result of Numerical analysis for optimum muffler is validated with Experimental analysis and it is perceived that, they are in good agreement with each other up to 94%. The cross verification of simulation and experimental results shows the confidence in above conclusion. Based on experiment and numerical simulation, it is proved that varying the diameter of extended inlet tube does affect Transmission Loss. Aim of the research is changing TL with varying inlet extension diameter and comparing the real-life component with FEA results. One aim highlights benefit of diameter variation on Transmission Loss and other leads positive conclusion that Computer Aided Engineering (CAE) are providing good accuracy in results.