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Noise Control: From Concept to Application

Colin H. Hansen, Kristy L. Hansen

Chapter 5

Sound Absorbing Materials - all with Video Answers

Educators


Chapter Questions

11:19

Problem 1

(a) For the tube shown in Figure 5.19, calculate the specific acoustic impedance looking into the left end of the tube at $400 \mathrm{~Hz}$ if the reflection coefficient of the surface of the sample at the right end of the tube is $0.75+0.3 \mathrm{j}$. The higher order mode cut-on frequency of the tube is $1200 \mathrm{~Hz}$ and the temperature of the air in the tube is $20^{\circ} \mathrm{C}$. In your analysis, let the surface of the sample be the origin of the coordinate system.
(b) Calculate the normal incidence sound absorption coefficient of the sample.
(c) Calculate the statistical absorption coefficient for the sample.
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Donald Albin
Donald Albin
Numerade Educator
02:12

Problem 2

The maximum sound pressure level measured in a $2.5 \mathrm{~cm}$ diameter impedance tube containing a test sample at the opposite end to a loudspeaker, generating sound at $500 \mathrm{~Hz}$, is $90 \mathrm{~dB}$ and the two minima closest to the test sample have values of 82 $\mathrm{dB}$ and $83 \mathrm{~dB}$, respectively. The distance from the face of the sample to the nearest pressure minimum is $0.1 \mathrm{~m}$.

(a) Derive an expression for the ratio, $(B / A)$, of the scalar amplitude of the reflected wave to that of the wave incident on the sample as a function of the difference between the maximum and extrapolated minimum sound pressure levels in the tube.
(b) Calculate the normal incidence absorption coefficient of the sample at $500 \mathrm{~Hz}$.
(c) Calculate the losses in the tube in $\mathrm{dB} / \mathrm{m}$ at $500 \mathrm{~Hz}$.

Arun Bana
Arun Bana
Numerade Educator
02:45

Problem 3

A small diameter tube with a loudspeaker mounted at one end may be used to measure the normal incidence absorption coefficient, $\alpha_n$, of a sample of material mounted at the other end. The quantity, $\alpha_n$, is defined as the ratio of the energy absorbed by the sample to that incident upon it. The energy reflection coefficient, $\left|R_p\right|^2$, is simply $1-\alpha_n$. For single frequency sound, use the solution to the wave equation to derive an expression for the total sound pressure amplitude as a function of axial location, $x$, in the tube and the pressure amplitude reflection coefficient, $R_p$, of the sample. Let the sample surface be at $x=0$ and the loudspeaker be at $x=L$. Assume a phase shift of $\beta$ between the waves incident and reflected from the sample.

Ajay Singhal
Ajay Singhal
Numerade Educator

Problem 4

Sound-absorbing material with a noise reduction coefficient of 0.8 has been specified for use in hanging sound absorbers in a noisy factory. You are offered rockwool material characterised by the sound absorption coefficients shown in Table 5.3. What is the NRC value?
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Problem 5

Find the mean Sabine absorption coefficient for a room of dimensions $6.84 \times 5.565$ $\times 4.72 \mathrm{~m}$ high, if the floor and ceiling have a mean absorption coefficient of 0.02 , the two smaller walls a coefficient of 0.05 and the large walls a coefficient of 0.06 .

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Problem 6

A loudspeaker is used to introduce sound into an impedance tube, $2.5 \mathrm{~m}$ long and 10 $\mathrm{cm}$ diameter, to determine the absorption coefficient (at $315 \mathrm{~Hz}$ ) of a sample placed at one end. The maximum measured sound pressure level in the tube is $99.0 \mathrm{~dB}$ and the levels of the two minima closest to the sample are 90.0 and $91.5 \mathrm{~dB}$. The distance between the surface of the sample and the first minimum in the tube is $0.15 \mathrm{~m}$.
(a) Calculate the normal incidence sound absorption coefficient of the sample.
(b) Calculate the sound intensity $\left(\mathrm{W} / \mathrm{m}^2\right)$ of the wave propagating towards the sample in the tube.
(c) Calculate the sound intensity ( $\mathrm{W} / \mathrm{m}^2$ ) of the wave propagating away from the sample (at the sample surface) in the tube.
(d) Calculate the acoustic power (W) dissipated by the sample.
(e) Calculate the acoustic power (W) dissipated in the tube.
(f) What will be the minimum continuous electrical power rating (W) required of the loudspeaker? State any assumptions that you make.

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03:16

Problem 7

A perforated sheet is used to cover a $100 \mathrm{~mm}$ thick blanket of rockwool inside a brick enclosure around a large item of equipment emitting a $500 \mathrm{~Hz}$ tone. The aim is to use the perforated sheet to maximise sound absorption at $500 \mathrm{~Hz}$. Determine the optimum percentage of open area of a steel perforated sheet, $3 \mathrm{~mm}$ thick with holes $3 \mathrm{~mm}$ in diameter.

Donald Albin
Donald Albin
Numerade Educator
03:25

Problem 8

In a rectangular shaped auditorium of dimensions $30 \mathrm{~m} \times 20 \mathrm{~m} \times 3 \mathrm{~m}$ high, the existing reverberation times at $20^{\circ} \mathrm{C}$ and $50 \%$ relative humidity are listed in Table 5.4. Using a combination of panel absorbers and $25 \mathrm{~mm}$ thick rockwool (covered with a thin layer of felt), determine how many square metres of the wall and ceiling surface you must cover with each type of absorption to achieve the reverberation times in the second line of the table. At higher frequencies, air absorption is likely to be a contributor and should be included. The absorption coefficients of the rockwool are listed in line 3 of the table.
table cant copy

Penny Riley
Penny Riley
Numerade Educator

Problem 9

A machine in a small factory produces the octave band sound power levels listed in line 1 of Table 5.5. The factory dimensions are $10 \mathrm{~m} \times 8 \mathrm{~m} \times 4 \mathrm{~m}$ high.
(a) Calculate the octave band reverberant field sound pressure levels at $20^{\circ} \mathrm{C}$ and $50 \%$ relative humidity if the average Sabine absorption coefficients of the room surfaces are as in line 2 of the table. These coefficients do not include air absorption (which may be calculated using the procedure outlined in Section 6.4.1).
(b) Calculate the overall reverberant field sound pressure level in $\mathrm{dBA}$ re $20 \mu \mathrm{Pa}$.
(c) Determine how much of the ceiling surface would need to be covered with 50 $\mathrm{mm}$ thick rockwool (sprayed with polyurethane and protected with a $25 \%$ open perforated panel) to reduce the overall reverberant sound pressure level by 5 $\mathrm{dBA}$. Absorption coefficients for this material are listed in line 3 of the table.
table cant copy

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