Chapter 6

Experimental Measurement of
Transmission Loss

As seen in the previous chapter the accuracy of optimization technique depends upon
many factors. There is need to validate the results with experimentation procedure to get
100% confidence level. This chapter is all about experimental set-up, experimentation
procedure and measurement.
The most common approach for measuring the transmission loss of a muffler is to
determine the incident power by decomposition theory and the transmitted power by the
plane wave approximation by using anechoic termination. But it is difficult to get fully
anechoic termination [12]. Thus another approach of two load method is used [110]. The
measured transmission loss values are compared with those obtained by the FEM method
demonstrating that transmission loss can be determined reliably with the experimental
set-up developed. The two load method is easier to employ for measuring transmission
loss.

6.1 Two Load Method

In the two load method, two loads should be different to keep results stable. Generally,
two loads can be two different length tubes, a single tube with and without absorbing
materials [110]. In the present work two loads were achieved by outlet tube with and
without absorbing material as shown in Figure 6.1.
The two load method is based on the transfer matrix approach. Using the transfer

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Figure 6.1: Two configurations and schematic model of a muffler
CHAPTER 6. EXPERIMENTAL MEASUREMENT OF TRANSMISSION LOSS
 CHAPTER 6. EXPERIMENTAL MEASUREMENT OF TRANSMISSION LOSS

matrix method, one can readily obtain transmission loss of any muffler by obtaining four
pole parameters from the four positions of microphones as shown in Figure 6.1.

6.2 Experimental Set-up

A schematic diagram of experimental set-up for calculating TL of simple expansion muf-
fler is shown in Figure 6.2. It consists of a noise generation system, noise propagation
system and noise measurement system. The TL is measured by transfer function method.
The set-up has the following main components.

• Impedance tube

• Data acquisition system

• Noise source with amplifier

• Sound pressure measuring microphones

Impedance tube is a rigid tube through which sound propagates and reflects from test
sample which results in creation of standing waves in it. It has measuring locations at
specific distances from test sample where the acoustic pressure is measured. A sound
source device is connected at one end of impedance tube and test muffler at the other
end. As we are interested in incident and transmitted wave, two impedance tubes are used
on either side of the muffler. The main purpose served by impedance tube is providing
guidance to sound wave as required for plane wave propagation.
The data acquisition system used is a four channel FFT analyzer (OROS OR34, 4
Channel) with an interface for the control and setting of analyzer. A fourier transformer
converts time signal data into frequency signal data and vice versa; an FFT rapidly com-
putes such transformations. As a result, FFT is widely used for many applications in
engineering and science.
Figure 6.3 shows OROS, 4 channel, compact, real time multi analyser along with
required instruments and accessories. OR34 is the synthesis of the ultimate 3 series tech-
nology, that integrates the best of noise and vibration analysis technology in an ultra
mobile instrument. It is low weight, portable and robust instrument which can be used
with laptop for intensive use.

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Figure 6.2: Schematic diagram of experimental set-up with its components
CHAPTER 6. EXPERIMENTAL MEASUREMENT OF TRANSMISSION LOSS
CHAPTER 6. EXPERIMENTAL MEASUREMENT OF TRANSMISSION LOSS

Figure 6.3: FFT analyzer and accessories

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Main features of FFT are as follows.

• Ultra-light: 1.4 kg

• Real-time bandwidth 40 kHz

• ± 10 V Inputs, 24 bits, ICP

• 100 Mbits/Ethernet

• AC/DC power supply

• 2 external triggers/tachometers inputs

• 1 generator output

FFT collects the pressure data from microphones (PCB 377C10 pressure field) and
feeds it to data recording storage system via BNC cable. FFT also has a single output
channel which is fed to speaker through analyzer. A random noise signal is generated in
the same analyzer and directed to the speaker (Ahuja-AU60) via amplifier (Ahuja SSB-
45EM). The reason behind using random noise (white noise) is that it contains equal
power density of noise for each frequency.
Sound source used is of high power to produce at least 110 dB of noise. Pressure field
microphones are used for measurement. The two microphones are sufficient as transfer
function method is used. Transfer function is evaluated for each set of readings.

6.3 Experimental Procedure

Experimentation for pressure measurement mainly consists of analyzer setting and data
processing for TL calculation. The experiment is performed for frequency range of 50 to
3400 Hz. The measurements are taken in two slots with two locations 1-1’ and 4-4’ (refer
Figure 6.2) respectively to cover desired frequency range [111]. The locations 1-2-3-4
are used for measuring pressure in frequency range 50-400 Hz, while the locations 1’-2-
3-4’ are used for measuring pressure in frequency range of 400-3400 Hz. The first set of
readings is taken for no load condition with both frequency ranges and same procedure is
repeated for with load condition. Two microphones are used for measurement, which are
sufficient for measurement of transfer function between sound pressures measured at two

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locations. One microphone is placed at location 3 and other placed at location 1, 2 and
4 respectively to get transfer function H31 , H32 and H34 with respective locations. All
other locations except locations where microphones are inserted are sealed with plugs to
avoid sound leakage. The sound leakage is tested and wax is used to seal these leaks. The
obtained transfer functions are then directly used in four-pole element calculations to get
TL.
A random noise signal is generated with frequency range 10 to 5 kHz. The speaker
noise spectrum is kept 10 to 15 dB higher than the background noise for all frequencies
of interest. The loudspeaker is operated for 5 to 10 minutes so that the temperature inside
the tube is stabilized. The sound leakage is tested and wax is used to seal these leaks.
The precaution is taken while changing the microphone to other location. Correction to
transfer function is added for considering the microphone mismatch.

p
Hc = Hij × Hji (6.1)

Hij(measured)
Hij(corrected) = (6.2)
Hc

This data is then post processed with the help of NVGate 7.0 in FFT module to get fre-
quency domain data. From frequency data transmission loss is calculated.

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6.4 Post Processing

By using two microphones (random excitation) data is collected from FFT. From the
data, transfer functions are calculated from the four positions of the microphones and
processed with the following calculations. Substituting these transfer functions in four
pole parameters transmission loss is calculated.
Neglecting flow of air, the four pole parameters for elements 1 − 2 can be expressed as
   
A12 B12 cos(kl12 ) iρcsin(kl12 )
 =  (6.3)
isin(kl12 )
C12 D12 ρc
cos(kl12 )

The four pole parameters for elements 2 − 3 can be expressed as

 
A23 B23
  (6.4)
C23 D23

where
∆34 (H32a H34b − H32b H34a ) + D34 (H32b − H32a )
A23 = (6.5)
∆(H34b − H34a )

B34 (H32a − H32b )

B23 = (6.6)
∆34 (H34b − H34a )

(H31a − A12 H32a )(∆34 H34b − D34 ) − (H31b − A12 H32b )(∆34 H34a )
C23 = (6.7)
B12 ∆34 (H34b − H34a )

B34 (H31a − H31b ) − A12 (H32b − H32a )

D23 = (6.8)
B12 ∆34 (H34b − H34a )

The term Hij represents transfer function between Pi and Pj (Hij ) = (Pj /Pi ). The four
pole parameters for elements 3 − 4 can be expressed as
   
A34 B34 cos(kl34 ) iρcsin(kl34 )
 =  (6.9)
isin(kl34 )
C34 D34 ρc
cos(kl34 )

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By cascading these matrices final transfer matrix is

     
A14 B14 A12 B12 A23 B23 A34 B34
 =    (6.10)
C14 D14 C12 D12 C23 D23 C34 D34

  
1  B14 
T L = 20 log10 A14 + + ρcC 14 + D 14
 (6.11)
2  ρc 

The actual test set-up with required components is shown in Figure 6.4 and 6.5. Two
configurations of set-up are used with respect to boundary conditions.

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CHAPTER 6. EXPERIMENTAL MEASUREMENT OF TRANSMISSION LOSS

Figure 6.4: Actual set-up without load

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CHAPTER 6. EXPERIMENTAL MEASUREMENT OF TRANSMISSION LOSS

Figure 6.5: Actual set-up with load

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6.5 Validation of Experimental Set-up

After preparing the set-up for the experimentation it is necessary that results of known
model are verified by the set-up to confirm the validity of experimental set-up.
Each reading is taken for time domain pressure signal with a recorder module of an-
alyzer which runs for a period of 100 sec. Figure 6.6 shows sample time domain signal
collected by data acquisition system from two microphones.

Figure 6.6: Time domain signal collected by data acquisition system

Inset of Figure 6.7 and Figure 6.8 show muffler geometry of central inlet, central
outlet muffler and central inlet, side outlet muffler. Figures also show comparison of
results of experiment with FEM (COMSOL) for these models. For both these models the
experimental results show good agreement with the numerical results.
From the results it can be concluded that from the developed experimental set-up it
is possible to measure the transmission loss of any muffler. The minor deviation of the
experimental results from the numerical results may be due to leakage of sound from the
surrounding or numerical error in computation.
The next chapter deals with results obtained in a variety of muffler configurations
leading to determination of an optimal design of a silencer using grid search method,

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Taguchi and ANOVA.

Figure 6.7: Comparison of results of experiment with FEM (COMSOL) for central inlet
central outlet muffler

Figure 6.8: Comparison of results of experiment with FEM (COMSOL) for central inlet
side outlet muffler

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