FORM 2
THE PATENTS ACT, 1970
(39 of 1970)
As amended by the Patents (Amendment) Act, 2005
&
The Patents Rules, 2003
As amended by the Patents (Amendment) Rules, 2006
COMPLETE SPECIFICATION
(See section 10 and rule 13)
TITLE OF THE INVENTION An exhaust muffler
APPLICANT
Mahindra & Mahindra Ltd., Gateway Building. Apollo Bunder, Mumbai 400 001, Maharashtra,
India, an Indian company
INVENTOR
Samant Sharad Ramkrishna, A/6, Shreekripa, Nandadeep Society, JP Naga'r, Road No. 5,
Goregaon (East), Mumbai, Pin 400063 Maharashtra, an Indian national
PREAMBLE TO THE DESCRIPTION
The following specification particularly describes the invention and the manner in which it is to
be performed:

FIELD OF THE INVENTION
[0001] The present invention relates generally to improvements in engine exhaust
mufflers.
DESCRIPTION OF THE BACKGROUND ART
[0002] In general, mufflers are distinguished in three categories, namely reactive
(reflective), absorptive (dissipative) and compound (reactive-absorptive) mufflers. A reactive muffler incorporates plurality of expansion chambers, perforated tubes and tortuous gas flow paths. It is more effective in attenuating lower and medium ranges of exhaust sound frequencies. However, reactive mufflers are less effective in attenuating higher ranges of frequencies. An absorptive muffler incorporates plurality of expansion chambers filled with sound absorbing material and perforated tube with straight through gas flow path. Absorptive mufflers are more effective in attenuating medium and higher ranges of frequencies of exhaust sound waves.
10003] Essentially, an exhaust muffler consists of a housing that has an inlet port at
an upstream end for entry of engine exhaust gases therein and an outlet port at the downstream end for exiting of the attenuated engine exhaust gases in the neighbouring atmosphere. Compared with other applications of muffler, design of exhaust muffler is very complex as it involves various design parameters for example, backpressure. Such backpressure results of obstruction to flow of engine exhaust gases due to baffles disposed along the flow path of exhaust gas. Unacceptable levels of developed backpressure tend to create negative effect on the engine performance and would therefore lead to high specific fuel consumption.
|0004] Thus, while designing of an exhaust muffler it becomes imperative that
besides the main intention of attenuating noise due care is taken to avoid formation of

unacceptable levels of backpressure in the exhaust system. To take care of this concern some
manufacturers have developed mufflers with a straight through pipe having perforations for entry
i and exit of the exhaust gas. The pipes are enclosed within a. shell for attenuating noise/sound
frequencies to desired level. However, in such configurations of exhaust muffler, working on
specific frequencies or dominant frequencies of exhaust gas sound wave spectrum may not be
accurate. Due to this, effectiveness of sound attenuation may not be satisfactory in all situations
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of engine applications.
[0005] However, in applications where backpressure is not considered as a principal
design parameter, the shell is partitioned into different chambers. The chambers may be completely or partially closed by providing openings in separating baffle plates. The shell is also provided with an inlet pipe for communicating exhaust gas with desired chambers and an outlet pipe for exiting the exhaust gas out of the muffler. Further, a ciesired number of perforated tubes may also be provided in the muffler for communicating the exhaust gas between different chambers. This particular configuration of the muffler is more efficient in attenuating the sound level but may cause more backpressure in the exhaust system of the engine due to increased resistance in flow path of the gas.
[0006] The existing mufflers have not been able to effectively attenuate dominant
lower range of sound frequencies along with their harmonics, some of the medium to higher range of sound frequencies of engine exhaust gas, and with minimum backpressure on engine. As the sound levels of the exhaust gases and exhaust gas back pressure on engine are inversely proportional to each other, designing of exhaust mufflers that takes dual functionality has been somewhat difficult. Hence, there is a need to design the exhaust muffler, which will effectively dampen broader spectrum of sound frequencies with minimum backpressure on engine.

SUMMARY OF THE INVENTION
[0007] Accordingly disclosed herein is an exhaust muffler couplable with an engine
exhaust manifold for receiving exhaust gases including an outer shell defined between a pair of opposite ends and including an inlet tube and an outlet tube, the inlet and outlet tubes partially insertable within the outer shell from mutually opposite directions through the opposite ends, the inlet tube introduces a partially attenuated exhaust gas downstream in the outer shell and positioned at a distance from the outlet tube, an expansion chamber disposed in fluid communication relationship with the inserted inlet tube and includes a diffuser plate disposed therein, the diffuser plate partitions the expansion chamber to define an interconnectable first and second expansion chambers, the diffuser plate allowing a substantially attenuated exhaust gas into the second expansion chamber, a perforated intermediate tube linearly arranged between the inlet and outlet tubes and positioned concentric to the outer shell, the intermediate tube disposed in fluid communication relationship with the second expansion chamber to partially receive the substantially attenuated exhaust gas, and a pair of perforated baffles mounted around the intermediate tube to define a partial resonator chamber formed between the intermediate tube and the inner surface of the outer shell, the partial resonator chamber having exposure of perforations of the intermediate tube to receive a first portion of the substantially attenuated exhaust gas, the partial resonator chamber disposed in fluid communication relationship with the second expansion chamber to receive remaining of the substantially attenuated exhaust gas therefrom, wherein the substantially attenuated exhaust gas from the partial resonating chamber is channelled downstream into the outlet tube.
[0008] In some embodiments, the inlet tube has an inner end that includes an
imperforated first baffle mounted thereon, the first baffle radially extending outwardly to contact

the inner surface of the outer shell thereby defining an inlet resonating chamber, and wherein the inlet tube has a plurality of equally spaced openings for providing fluid communication between the exhaust gas and the inlet resonating chamber.
[0009] In some embodiments, the outlet tube has an inner end that includes an
imperforated second baffle mounted thereon, the second baffle radially extending outwardly to contact the inner surface of the outer shell thereby defining an outlet resonating chamber, and wherein the outlet tube has a plurality of equally spaced openings for providing fluid communication between the substantially attenuated exhaust gas and the outlet resonating
chamber.
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[0010] In some embodiments, the number of the exposed perforations of the
intermediate tube within the partial resonating chamber is greater than the surface area of the
exposed perforations within the third expansion chamber.
[0011] In some embodiments, the diffuser plate is circular in shape and includes a
plurality of openings formed therein, and wherein the plurality of openings is arranged in multiple circular configurations, the multiple circular configurations concentric with the circular diffuser plate.
[0012] It is to be understood that both the foregoing general description and the
following detailed description of the present embodiments of the invention are intended to provide an overview or framework for understanding the nature and character of the invention as it is claimed. The accompanying drawings are included to provide a further understanding of the
invention and are incorporated into and constitute a part of this specification. The drawings
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illustrate various embodiments of the invention and together with the description serve to explain the principles and operation of the invention.

A BRIEF DESCRIPTION OF THE DRAWINGS
[0013] The above-mentioned and other features and advantages of the various
embodiments of the invention, and the manner of attaining them, will become more apparent and will be better understood by reference to the accompanying drawings, wherein:
[0014] FIG. 1 is a longitudinal cut sectional view of an exhaust muffler according to
an embodiment of the present invention;
[0015] FIG. 2a is a cross sectional view of the exhaust muffler of FIG. 1 taken along
lines A-A and E-E;
[0016] FIG. 2b is a cross sectional view of the exhaust muffler of FIG. 1 taken along
line B-B; and
[0017] FIG. 2c is a cross sectional view of the exhaust muffler of FIG. 1 taken along
lines C-C and D-D.
DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS
[0018] FIG. 1 illustrates an exhaust muffler 100 according to an embodiment of the
present invention. The exhaust muffler 100 includes an outer shell 102 that is shown to be horizontally disposed. The outer shell 102 has a length that extends between a pair of open opposite ends 104, 106. The outer shell 102 has an inner surface 108, an outer surface 110, and a predetermined thickness extending between the outer surface 110 and the inner surface 108. Further, the outer shell 102 has a predefined inner diameter, outer diameter, and formed of a predetermined cross-sectional area. Preferably, the open opposite ends 104, 106 of the outer shell 102 are fixedly closed by disposing an inlet cap 112 and an outlet cap 114 at the opposite ends 104, 106, respectively. As seen in FIG. 1, each of the inlet cap 112 and the outlet cap 114 has a

central opening (not shown) formed along its thickness. Depending on the design considerations, the outer shell 102 of the exhaust muffler 100 has a cylindrical shape, however other shapes of the outer shell 102 compatible with the working of the exhaust muffler 100 may also be considered to be within the scope of the present invention.
[0019] As seen in FIG. 1. an inlet tube 116 is shown to be partially insertable within
the outer shell 102 through the central opening formed within the inlet cap 112. Similarly, an outlet tube 118 is shown to be partially insertable within the outer shell 102 through the central opening formed within the outlet cap 114. Both the inlet tube 116 and the outlet tube 118 extends between an inner end 120 and an outer end (not shown), wherein the inner end 120 is disposed within the outer shell 102 whereas the outer end is disposed outside the outer shell 102. An outer diameter of both the inlet tube 116 and the outlet tube 118 is designed to be smaller than the inner diameter of the outer shell 102. This is to ensure easy insertion of the inlet and outlet tubes 116, 118 within the outer shell 102 through the inlet and outlet caps 112, 114. Preferably, both the inlet and outlet tubes 116, 118 are disposed concentric to the outer shell 102. Further, both the inlet and outlet tubes 116, 118 are positioned at a predetermined radial distance from the inner surface 108 thereof. Furthermore, as noted in FIG. 1, both the inlet tube 116 as well as the outlet tube 118 are disposed in spaced apart relationship with each other. Preferably, both the inlet and the outlet tubes 116, 118 are hollow and have a cylindrical shape, however the inlet and outlet tubes 116, 118 may also be formed of other compatible shapes and considered to be within the scope of the present invention,
[0020] The inlet tube 1J 6 may be coupled to an engine exhaust manifold for drawing
in exhaust gas from an engine and for introducing the exhaust gas downstream within the outer shell 102. Generally, the exhaust gas generated by the engine has sound waves of specific

frequencies ranges and when introduced in muffling devices, exerts significant backpressure on the engine. The sound waves having such frequency levels need to be attenuated without compromising on the back pressure so that these does not adversely affect the performance of the engine. Precisely for this reason, exhaust muffler 100 are constructed to have various sections that performs sound attenuation without generating unacceptable levels of backpressure.
[0021] Further, as seen in FIG. 1, the inner end 120 of both the inlet and outlet tubes
116, 118 have an imperforated baffle 122 mounted thereon (also refer FIG. 2a). The imperforated baffle 122 extends radially outward to contact the inner surface 108 of the outer shell 102 so as to define an enclosed space. For the purpose of the specification, this enclosed space formed between the inlet tube 116 and the outer shell 102 is referred to as an inlet resonating chamber 124. In a similar manner, the imperforated baffle 122 mounted on the inner end 120 of the outlet tube 118 also extends radially outward to contact the inner surface 108 of the outer shell 102 so as to define another enclosed space, in the following description, this enclosed space is referred to as an outlet resonating chamber 126. The insertable portion of the inlet tube 116 and the outlet tube 118, as seen in FIG. 1, has a plurality of equally spaced openings 128 formed on an outer surface thereof and arranged in a circular configuration. The plurality of equally spaced openings 128 formed on the inlet tube 116 allows a portion of the exhaust gas (shown by arrows), of a particular frequency, to be introduced in the inlet resonating chamber 124. The inlet resonating chamber 124 attenuates a particular specific frequency of the exhaust gas sound waves. Partially attenuated exhaust gas or a remaining portion of the exhaust gas flows downstream within the exhaust muffler.
[0022] An expansion chamber 130 is located adjacent to the inlet resonating chamber
124 and arranged to be in fluid communication with the inlet tube 116 in a manner shown in

FIG. 1. The expansion chamber 130 includes a diffuser plate 132 positionable therein that separates the expansion chamber 130 into a first expansion chamber 134 and a second expansion chamber 136. The diffuser plate 132 has a plurality of slots 138 formed along its thickness and provides a common boundary wall 140 between the first and the second expansion chambers 134, 136. As such, the first expansion chamber 134 and the second expansion chamber 136 are interconnected with each other so as to allow fluid communication therebetween. Preferably, as seen in FIG. 1, the inlet resonating chamber 124 and the first expansion chamber 134 also have a partially open common boundary wall 142, The common boundary wall 142 is formed from the imperforated baffle 122 and the inner end 120 of the inlet tube 116. However, in another embodiment of the present invention, the inner end 120 may extend into the first expansion chamber 134 and therefore the common boundary wall 142 will only comprise of the imperforated baffle 122. This embodiment should be considered to be within the scope of the present invention.
[0023] FIG. 2b shows a cross-sectional view of the diffuser plate 132 positioned
within the outer shell 102 of the exhaust muffler 100 taken along a plane B-B, as shown in FIG. 1. Preferably, the diffuser plate 132 is circular in shape and has a thickness defined between an upstream surface and a downstream surface. Diameter of the diffuser plate 132 is chosen in such a way the diffuser plate 132 is tightly fitted within the outer shell 102 and maintains a positive contact with the inner surface 108 thereof. Further, the plurality of slots 138 formed within the diffuser plate 132 is arranged in multiple circular configurations. Each of the circular configurations is concentric to the circular shaped diffuser plate 132. Preferably, the number as well as the diameter of the slots 138 is chosen in such a way that the area of the plurality of slots 138 is greater than the cross-sectional area of the inlet tube 116. This ensures that the exhaust gas

passes with least resistance through the diffuser plate 132 and accordingly exerts minimum exhaust backpressure on the engine. Preferably, the plurality of slots 138 is equally spaced from each other and is preferably, circular in shape. However, in various other embodiments the plurality of slots 138 may not be equally spaced from each other and the plurality of slots 138 may be formed of some other shape. All such embodiments should be considered to be within the scope of the present invention.
[0024] Partially attenuated exhaust gas having varying frequencies is channelled
within the first expansion chamber 134. The partially attenuated exhaust gas. apart from being expanded therein, is obstructed by the diffuser plate 132. The diffuser plate 132 performs two functions within the expansion chamber. First, the diffuser plate 132 reflects a substantial portion of sound waves of a particular frequency in the upstream direction. Second, due to this reflection, the partially attenuated exhaust gas is converted into substantially attenuated exhaust gas (shown by arrows) which is then introduced in the second expansion chamber 136, The substantially attenuated exhaust gas further expands within the second expansion chamber 136.
[0025] FIG. 1 also shows an intermediate tube 144 linearly arranged in between the
inlet tube 116 and outlet tube 118 and disposed in fluid communication with the second expansion chamber 136. Preferably, the intermediate tube 144 is positioned concentric to the outer shell 102. The intermediate tube 144 extends between an upstream 'end 146 and a downstream end 148 and formed of a predetermined length. Further, the intermediate tube 144 has a central opening 150 defined by an inner surface 152 of the intermediate tube 144. The central opening ! 50 opens at the upstream end 146 and extends towards the downstream end 148 of the intermediate tube 144. However, the downstream end 148 of the intermediate tube 144 is closed. The central opening 150 a diameter of a predetermined value. Furthermore, the

intermediate tube 144 also includes perforations 154 formed along its thickness and uniformly distributed along the entire length of the perforated body. Preferably, the perforations 154 are formed in a first region 156 and an adjacently formed second region 158 of the intermediate tube 144. Depending upon the design considerations, the number of perforations 154 formed in the first region 156 is greater than the number of perforations 154 formed in the second region 158.
[0026] A pair of circular baffles is mounted on an outer surface 160 of the
intermediate tube 144, as shown in FIG. 1. Preferably, a first baffle 162 is mounted on the upstream end 146 of the intermediate tube 144 whereas a second baffle 164 is positioned at a distance from the first baffle 162. Preferably, the second baffle 164 is mounted on the outer surface 160in a manner so as to divide the first region 156 of perforation from the second region 158. Further, each of the first and the second baffles 162, 164 also extends radially outward to contact the inner surface 108 of the outer shell 102 thereby defining a partial resonator chamber 166 in between the outer surface 160 of the intermediate tube 144 and the outer shell 102. Preferably, the first and the second baffles 162, 164 also have a plurality of equally spaced openings 168 formed therein and arranged preferably in at least one circular configuration (See FIG. 2c). Furthermore, the partial resonator chamber 166 and the second expansion chamber 136 have a common boundary 170. This common boundary is formed of the open upstream end 146 of the intermediate tube 144 and the first baffle 162 having plurality of equally spaced openings.
[0027] As seen in FIG. 1, the second baffle 164 and the imperforated baffle 122
mounted on the inner end 120 of the exhaust tube define a third expansion chamber 172, which shares common boundaries 174 with the partial resonator chamber 166 and the outlet resonating chamber 126, respectively. Further, as seen in FIG. 1, a portion of the intermediate tube 144 having the perforations 154 of the second region 158 is also available within the third expansion

chamber 172. As seen, the third expansion chamber 172 is in fluid communication with the partial resonator chamber 166 and the intermediate tube 144, respectively. Additionally, as seen in FIG. I, one of the common boundaries that the third expansion chamber 172 shares with the outlet resonating chamber ]26 has exposure of the inner end 120 of the outlet tube ] 18. Thus, the third expansion chamber 172 is also disposed in fluid communication with the outlet tube 118.
[0028] The second expansion chamber 136 is in fluid communication with both the
intermediate tube 144 as well as the partial resonator chamber 166 (See FIG. 1). So, the substantially attenuated exhaust gas available within the second expansion chamber 136 finds two ways to escape from the second expansion chamber 136. First, the substantially attenuated exhaust gas is partially received within the intermediate tube 144 through the central opening 150 of the intermediate tube 144. However, due to larger number of the perforations 154 present in the first region 156 than in the second region 158, a first greater portion of the substantially attenuated exhaust gas is channelled within the partial resonator chamber 166 through the perforations 154 exposed therein. Second, the remaining portion of the substantially attenuated exhaust gas enters the partial resonator chamber 166 through the plurality of openings 168 formed within the first baffle 162. Accordingly, a second smaller portion of the substantially attenuated exhaust gas enters the third expansion chamber 172 through the perforations 154 present within the second region 158 and exposed within the third expansion chamber 172. Thus, the size and the number of holes formed on the first and the second regions 156, 158. respectively, determine the corresponding amount of substantially attenuated exhaust entering the partial resonator chamber 166 and the third expansion chamber 172. The size and number of the perforations !54 of the intermediate tube 144 as well as that of the openings 168 of the first

and second baffles 162, 164 are chosen in such a manner that the constructional features of the exhaust muffler 100 exert relatively less backpressure on the engine exhaust manifold.
[0029] Within the partial resonator chamber 166 the substantially attenuated exhaust
gas, received through the intermediate tube 144 and the second expansion chamber 136,
respectively, meets at right angles (See FIG. 1) to each other and as a skilled person would know.
this further attenuates the substantially attenuated exhaust gas. The substantially attenuated
exhaust gas available within the partial resonator chamber 166, as seen in'FIG. 1. is also
channelled within the third expansion chamber 172 through the plurality of openings 168 formed
within second baffle 164. This substantially attenuated exhaust gas again m'eets the second
portion of the attenuated gas received within the third expansion chamber 172 at right angles to
further attenuate the substantially attenuated exhaust gas.
[0030] Referring again to FIG. I, the substantially attenuated exhaust gas available
within the third expansion chamber 172 is then introduced within the outlet tube 118 through the inner end 120 thereof. The diameter of the outlet tube is chosen in such a manner that the exhaust gas exerts minimum backpressure on the engine to which it is coupled. Further, 'a predetermined amount of this substantially attenuated exhaust gas enters within the outlet resonating chamber 126 through the equally spaced openings 128. The remaining substantially attenuated exhaust
gas exits the exhaust muffler 100 in the neighbouring atmosphere. Sound waves from the
substantially attenuated exhaust gas interact with the second resonating chamber. Preferably, the
second resonating chamber attenuates the dominant frequencies of the exhaust gas sound waves
attenuated in the first resonating chamber. The imperforated baffle 122 mounted on inner ends
120 of both the inlet tube 116 and the outlet tube 118 also provides strength to the inlet tube and
the outlet tube against the outer shell 102 of the exhaust muffler.

[0031] An experiment was conducted on the exhaust muffler, as described in the
various above described embodiments, and the result that was received out of the test is suggestive of the fact that the exhaust muffler 100 has advantages over the existing muffler. According to the experiment, the exhaust muffler 100 was coupled with a 4 cylinder, naturally
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aspirated, 45 HP engine. The results that the experiment showed up were that the exhaust backpressure was reduced to 22 mbar. Due to this reduction in backpressure, specific fuel consumption of the engine was reduced to 173 gm/HP-Hour. Further, the Engine exhaust sound level at bystander ear level was also reduced to 84 db and sound level at operator ear level was reduced to 94 db.
[0032] The above mentioned embodiments of the exhaust muffler 100 find major
application in off-road vehicles. So, for using the exhaust muffler 100 with the off-road vehicles, the inlet pipe of the off-road vehicle is mounted to a stub pipe (not shown) of an exhaust manifold which is coupled to an engine (not shown) of the off-road vehicle. However, with little modifications in the above described exhaust muffler 100 for example, perforations formed on the inlet and outlet tubes 116, 118, volumes of different chambers, altering size of the diffuser piate 132 and its slots 138, additionally by providing sound absorbing material, the exhaust muffler 100 may also be easily and effectively used in other automotive vehicles such as, on -road vehicles earth movers, and the like. All such variations should be considered to be within the scope of the present invention.
[0033| It will be apparent to those skilled in the art that various modifications and
variations can be made to the present invention without departing from the spirit and scope of the invention. Thus it is intended that the present invention cover the modifications and variations of this invention provided they come within the scope of the appended claims and their equivalents.

We Claim:
1. An exhaust muffler couplable with an engine exhaust manifold for receiving exhaust gases
comprising:
an outer shell defined between a pair of opposite ends and including an inlet tube and an outlet tube, the inlet and outlet tubes partially insertable within the outer shell from mutually opposite directions through the opposite ends, the inlet tube introduces a partially attenuated exhaust gas downstream in the outer shell and positioned at a distance from the outlet tube;
an expansion chamber disposed in fluid communication relationship with the inserted inlet tube and includes a diffuser plate disposed therein, the diffuser plate partitions the expansion chamber to define.an interconnectable first and second expansion chambers, the diffuser plate allowing a substantially attenuated exhaust gas into the second expansion chamber;
a perforated intermediate tube linearly arranged between the inlet and outlet tubes and
positioned concentric to the outer she.ll. the intermediate tube disposed in fluid communication
relationship with the second expansion chamber to partially receive the substantially attenuated
exhaust gas; and
a pair of perforated baffles mounted around the intermediate tube to define a partial resonator chamber formed between the intermediate tube and the inner surface of the outer shell, the partial resonator chamber having exposure of perforations of the intermediate tube to receive a first portion of the substantially attenuated exhaust gas, the partial resonator chamber disposed in fluid communication relationship with the second expansion chamber to receive remaining of the substantially attenuated exhaust gas therefrom,
wherein the substantially attenuated exhaust gas from the partial resonating chamber is channelled downstream into the outlet tube.

2. The exhaust muffler according to claim 1, wherein the inlet tube has an inner end that includes an imperforated first baffle mounted thereon, the first baffle radially extending outwardly to contact the inner surface of the outer shell thereby defining an inlet resonating chamber, and wherein the inlet tube has a plurality of equally spaced openings for providing fluid communication between the exhaust gas and the inlet resonating chamber.
3. The exhaust muffler according to claim 1-, wherein the outlet tube has an inner end that
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includes an imperforated second baffle mounted thereon, the second baffle radially extending outwardly to contact the inner surface of the outer shell thereby defining an outlet resonating chamber, and wherein the outlet tube has a plurality of equally spaced openings for providing fluid communication between the substantially attenuated exhaust gas and the outlet resonating chamber.
4. The exhaust muffler according to claim I, wherein the substantially attenuated gas from the partial resonating chamber is introduced into a third expansion chamber via one of the perforated baffles, the third expansion chamber located adjacent to the partial resonator chamber and has exposure of perforations of the intermediate tube for providing a second portion of the substantially attenuated exhaust gas,
5. The exhaust muffler according to claim 4, wherein the number of the exposed perforations of the intermediate tube within the partial resonating chamber is greater than the number of the exposed perforations within the third expansion chamber.

6. The exhaust muffler according to claim 1, wherein the diffuser plate is circular in shape and
includes a plurality of openings formed therein, and wherein the plurality of openings is arranged
in multiple circular configurations, the multiple circular configurations concentric with the
circular diffuser plate.
7. The exhaust muffler according to claim 6, wherein the area of the plurality of openings formed within the diffuser plate is greater than the cross-sectional area of the inlet pipe.
8. The exhaust muffler according to claim 6, wherein the plurality of openings are equally spaced with each other and formed to have a circular shape.