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Noise Control: From Concept to Application

Colin H. Hansen, Kristy L. Hansen

Chapter 8

Muffling Devices - all with Video Answers

Educators

Chapter Questions

02:13

Problem 1

What is the main difference between a reactive and dissipative silencer?

Saman Zulfiqar
Saman Zulfiqar
Numerade Educator
02:34

Problem 2

We wish to calculate the extent of speech privacy (using Table 2.10) between two offices that share a common partition of area $10 \mathrm{~m}^2$. Each office has a suspended ceiling and the partition separating the offices continues above the suspended ceiling to the floor above. There is an unlined air conditioning duct that extends a distance of $5 \mathrm{~m}$ above each office and penetrates the partition above the suspended ceiling. The penetration may be considered to be well sealed. The duct wall thickness is $0.6 \mathrm{~mm}$ and the cross-sectional dimensions are $2 \mathrm{~m}$ wide $\times 1 \mathrm{~m}$ high. There is one air conditioning outlet of dimensions $0.2 \mathrm{~m} \times 0.2 \mathrm{~m}$ in each office. The configuration is illustrated in Figure 8.53. Partition, ceiling and air conditioning outlet TL data are listed in Table 8.21 . In the table, the TL data for the air conditioning outlets, represent the combined reduction for sound power entering the outlet in the source room to sound power radiated from the outlet in the receiver room. Follow the calculation steps listed below the assumptions to find the speech privacy condition. What would be the best way to improve the speech privacy if it is inadequate?
figure cant copy
TABLE 8.21 TL data for Problem 2
$$
\begin{array}{cccccccc}
\begin{array}{c}
\text { Frequency } \\
(\mathrm{Hz})
\end{array} & \mathrm{TL}_{\text {wall }} & \text { TL }_{\text {ceiling }} & \text { TL }_{\text {outlet }} & \begin{array}{c}
\text { Frequency } \\
(\mathrm{Hz})
\end{array} & \text { TL }_{\text {wall }} & \text { TL }_{\text {ceiling }} & \text { TL }_{\text {outlet }} \\
\hline 100 & 24 & 2 & 15 & 630 & 45 & 3 & 18 \\
125 & 27 & 2 & 15 & 800 & 44 & 3 & 19 \\
160 & 31 & 2 & 15 & 1000 & 43 & 3 & 19 \\
200 & 35 & 2 & 15 & 1250 & 44 & 3 & 20 \\
250 & 39 & 2 & 16 & 1600 & 45 & 3 & 20 \\
315 & 42 & 2 & 16 & 2000 & 47 & 3 & 20 \\
400 & 44 & 2 & 17 & 2500 & 49 & 3 & 20 \\
500 & 46 & 3 & 17 & 3150 & 51 & 3 & 20
\end{array}
$$
You may make the following additional assumptions:
• Sound is incident on and radiates from only the bottom of the duct – not the sides or top.
• There is a substantial partition in the ceiling space to reduce sound transmission
from one office to the next sufficiently so that the sound transmission through
this part of the partition can be ignored.
• Attenuation of the sound propagating in the duct is negligible.
• The ambient noise level in each office due to non-speech noise sources is 35 dBA.
(a) For each 1/3-octave band from 100 Hz to 3150 Hz, calculate the difference in
sound power level incident on the outside of the air conditioning duct in the
source office and the sound power level propagating in one direction inside the
duct.
(b) Calculate the difference in sound power level propagating in one direction inside
the duct and the sound power level radiated into the receiving office.
(c) For each 1/3-octave band from 100 Hz to 3150 Hz, add twice the ceiling TL to
the sum of items 1 and 2 to obtain the TL for air conditioning duct transmission.
(d) Combine the TL for the wall, duct and air conditioning outlets (one in each
room), taking into account the relative areas associated with each, to find the
overall TL in each frequency band.
(e) Find the overall TL averaged over all frequency bands from 100 Hz to 3150 Hz.
Tabulate all results.
(f) Add the average overall TL to the ambient noise level and use this result to enter
Table 2.10 to find the speech privacy condition.
(g) Look at the relative values in the tabulated results to determine what would
increase the speech privacy rating.

Chai Santi
Chai Santi
Numerade Educator
08:07

Problem 3

For a machine enclosure to be ventilated with a cooling fan, design a lined duct muffler (for the $500 \mathrm{~Hz} 1 / 3$-octave band only) that will be mounted on the enclosure to supply air to the cooling fan, such that its length is as short as possible. The maximum allowed external cross-sectional dimensions of the duct are $400 \mathrm{~mm} \times 400$ $\mathrm{mm}$ and the maximum allowed air flow speed is $7 \mathrm{~m} / \mathrm{s}$. The required volume of airflow is $0.263 \mathrm{~m}^3 / \mathrm{s}$. You may use acoustic material with no plastic liner and no internal solid partitions but with a $30 \%$ open area perforated steel facing.

Khoobchandra Agrawal
Khoobchandra Agrawal
Numerade Educator
04:58

Problem 4

Calculate the reduction in sound pressure level in the $1000 \mathrm{~Hz} 1 / 3$-octave band at an observer location $1.5 \mathrm{~m}$ above the ground at a horizontal distance of $35 \mathrm{~m}$ from an industrial fan exhaust located $2 \mathrm{~m}$ above the ground, if an unlined $20 \mathrm{~m}$ long vertical exhaust stack of $0.4 \mathrm{~m}$ diameter is added to the exhaust and the exhaust is re-orientated from pointing directly at the observer to pointing up vertically. Ignore any excess attenuation effects except for the ground effect. However, you may assume that the ground between the exhaust and the measurement location is concrete and there is incoherent addition of the direct and ground-reflected waves at the observer. The temperature of the air exiting the exhaust stack is $20^{\circ} \mathrm{C}$. Ignore sound radiation from the exhaust stack walls. Use the theoretical exhaust stack directivity curves calculated using the Davy model.

Keshav Singh
Keshav Singh
Numerade Educator

Problem 5

The tube shown in Figure 8.54 is terminated at the right end by a perforated plate of thickness $1.6 \mathrm{~mm}$, open area $10 \%$ and hole diameter $2.0 \mathrm{~mm}$. A $300 \mathrm{~Hz}$, sound introduced into the left end of the tube produces a standing wave in the tube which has a standing wave ratio of $15 \mathrm{~dB}$ when the temperature in the tube is $20^{\circ} \mathrm{C}$.
(a) What is the normal incidence sound absorption coefficient of the perforated sheet at $300 \mathrm{~Hz}$ for sound incident from the left hand side?
figure cant copy
(b) What is the effective length of the holes in the perforated sheet if the Mach
number, M, of the cross flow over the perforated panel is 0.15?
(c) Calculate the acoustic impedance that would be expected to be measured by
measuring the distance from the inside edge of the perforated sheet, of the first
sound pressure level minimum in the tube if the Mach number, M, of the cross
flow over the perforated panel is 0.15 and if the acoustic resistance of each hole
in the perforated panel consists only of the contribution from this flow. You may
ignore the contribution to the impedance of the mass of the steel part of the
perforated panel.

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Problem 6

Consider the muffler system shown in Figure 8.55.
figure cant copy
(a) Assuming that the load impedance is included with item 7 and that the impedances of each element may be treated as lumped, draw an equivalent electrical circuit for the system illustrated.
(b) Derive an expression (in terms of the impedances, $Z_i, i=1, \ldots .7$, of each of the above 7 elements) for the Insertion Loss if the shaded source on the left is a constant volume-velocity source.

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02:34

Problem 7

An acoustic enclosure requires a ventilation system. To exhaust the air, a dissipative muffler in the form of a duct lined on all four sides is needed. An attenuation of $9 \mathrm{~dB}$ is needed at $125 \mathrm{~Hz}, 15 \mathrm{~dB}$ at $1000 \mathrm{~Hz}$ and $15 \mathrm{~dB}$ at $2000 \mathrm{~Hz}$. Calculate the length of lined square section duct needed if the maximum allowed outer cross-sectional area is $1 \mathrm{~m}^2$ and the minimum allowed internal cross-sectional area is $0.25 \mathrm{~m}^2$.

Chai Santi
Chai Santi
Numerade Educator

Problem 8

A plenum chamber shaped like a rectangular parallelepiped is to be included in an air-conditioning duct that has a noise problem in the $630 \mathrm{~Hz} 1 / 3$-octave band. The allowable space limits the cross-sectional size of the plenum chamber to $3 \mathrm{~m} \times 3 \mathrm{~m}$. The length is $4 \mathrm{~m}$. The inlet and outlet ducts have cross-sectional dimensions of 0.5 $\mathrm{m} \times 0.5 \mathrm{~m}$ and the inlet duct enters the chamber at one end at the centre top, while the outlet duct is attached at the other end at the centre bottom.
(a) Sketch the arrangement.
(b) If the mean Sabine absorption coefficient of the chamber walls is 0.2 in the $630 \mathrm{~Hz}$ $1 / 3$-octave band, what would be the reduction in sound power level transmitted to the exit duct as a result of inserting the chamber, assuming that the plenum chamber does not affect the sound power output of the source and that the downstream duct is sufficiently long that the amplitudes of the waves reflected back upstream from the duct exit are negligible at the exit of the plenum chamber (use both the Wells and ASHRAE methods)?
(c) What would be the increase in noise reduction if the Sabine absorption coefficient of the chamber were increased to 0.5 (use both the Wells and ASHRAE methods)?
(d) How much additional noise reduction (for the configuration in part (a) above) would be obtained if a partial partition were placed in the centre of the chamber so that the line of sight between the inlet and outlet openings in the plenum chamber no longer existed (use only the Wells method)? The partition extends the full width of the chamber and only has an opening, $0.2 \mathrm{~m}$ high, at the bottom.
(e) If the sound pressure level in the upstream duct were $90 \mathrm{~dB}$ in the $630 \mathrm{~Hz}$ octave band, what would be the sound pressure level in the downstream duct for the configuration on part (b)? Use both the Wells and ASHRAE methods.

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