Acoustic principles using mathematical analysis
Order Instructions:
Main Assignment Questions (90% of unit weighting)
AR 50345
The objective of the course work is to demonstrate an understanding of the acoustic principles discussed during the unit week. This can be done in the form of mathematical analysis, an essay style answer or as bullet points. Marks against each section are
indicated as are word lengths, as appropriate.
Q1 a) Please outline your understanding of the following acoustic terms, (using 50 to 100 words each). Credit will be given for each key requirement or unique feature included. Additionally, please indicate where each of these terms are used in the field of acoustics: (10 marks)
Free field
Diffused field
dB
dBA
NR
W-weighting
Rw
R
0
w
(apparent sound reduction)
Dw
Dn
T
w
b) Please provide both a hand calculation and excel spread sheet
calculating the following.
(15 marks)
dBA for the following spectra:
32Hz 64Hz 125Hz 250Hz 500Hz 1kHz 2kHz 4kHz 8kHz
30 30 30 – – – – – — – – 30 35 36 50 36 35
65 83 90 75 43 35 – – — 10 10 10 10 10 10 10 -NR:
32Hz 64Hz 125Hz 250Hz 500Hz 1kHz 2kHz 4kHz 8kHz
30 30 30 – – – – – — – – 30 35 36 50 36 35
65 83 90 75 43 35 – – — 10 10 10 10 10 10 10 -Rw
(spread sheet only) for the following spectra:
125Hz 250Hz 500Hz 1kHz 2kHz
16 24 33 42 43
39 44 56 67 74
38 37 48 64 78
34 39 51 60 68
2 of 4 AR50345
Q2 a) Please explain, or undertake mathematically, how one determines
the composite sound reduction of the following two elements. The area of element 1 should be taken as 9m 2 with an Rw of 40dB.
The second element has an area of 2m 2 and an R w of 30dB.
(5 marks)
b) Use the above explanation to show how the 10dB rule works, i.e.
“There is no benefit in increasing the sound reduction of the larger element more than 10 dB over the smaller element which has a lesser sound reduction.” (5 marks)
Q3 a) Calculate the sound reduction of a facade comprising of: (6 marks)
10m 2 of glass/windows 20m 2 of brickwork and a 5m
2 spandrel panel
The area of the room should be taken as 200m 2
. The reverberation time in this room is equal to 0.7 seconds. Please state the sound reduction used for each element making up the facade and the source of this information.
b) Repeat this exercise but now include a plot of the combined sound reduction when an open window is placed in the facade.
This window has an effective open area of 1m by 0.01m; this window is then further opened in increments to a final effective open area of 1mby 0.25m. The area of the window should be taken out of the glazed element within the facade. (4 marks)
Q4 Sustainability and Acoustics. (20 marks)
Acoustics and sustainability are not often referred to in tandem. On the other hand, it has been shown that there are many links between these two subjects. Please provide your thoughts with respect to the links between acoustics and sustainable building
design.
Please also provide a review of products which are available to enhance the acoustic performance of a vented facade. This information can also be complemented with acoustics details relating to cross ventilation. (500 words) 3 of 4 AR50345
Q5 Reverberation time calculation. (15 marks)
Compose an Excel spreadsheet that calculates the absorption coefficient of the sound absorbing panels in the East Building classroom from 125 Hz to 4000 Hz (octave bands). To do this you should use the test data from the practical session for the empty room (with tables and chairs removed). This data is as follows:
Octave Band Centre Frequency, Hz
125 250 500 1000 2000 4000
Measured Average RT Empty
(Seconds)
0.9 0.8 0.9 0.7 0.7 0.6
The room dimensions may be taken as 13.2W x 5.2D x 3.2H.
There are 65 absorptive panels each with an area of 0.45mx 0.6m. You will need to estimate the absorption coefficients for the other surfaces (e.g. carpet, concrete soffit, glass facade, studwork
walls and doors and use these to calculate the absorption coefficient of the panels. What effect would distributing the panels throughout the room have compared with locating the panels in one large area?
Q6 A building has two items of plant on the roof, (a kitchen extract fan and a kitchen supply fan). The sound power levels of the units are as follows: (20 marks)
Frequency 63Hz 125Hz 250Hz 500Hz 1kHz 2kHz 4kHz
Kitchen Extract 84 85 83 80 78 76 72
Kitchen Supply 76 78 78 75 73 70 68
Calculate the A-weighted sound pressure level (dBA) at the nearest house, which is approximately 25m from the plant. You may assume that the kitchen extract fan is screened by a parapet that just obscures the line of sight. The kitchen supply fan is un-screened. You should clearly identify each step in your calculation or submit a spreadsheet.
SAMPLE ANSWER
Question 1: Part B
dBA for the following spectra:
| 32 Hz | 64 Hz | 125 Hz | 250 Hz | 500 Hz | 1 kHz | 2 kHz | 4 kHz | 8 kHz |
| 30 | 30 | 30 | 45 | 20 | 30 | 20 | 25 | 25 |
| 35 | 53 | 60 | 30 | 35 | 30 | 50 | 36 | 35 |
| 65 | 83 | 90 | 75 | 43 | 35 | 30 | 45 | 55 |
| 10 | 10 | 10 | 10 | 10 | 10 | 10 | 10 | 10 |
NR for the following spectra:
| 32 Hz | 64 Hz | 125 Hz | 250 Hz | 500 Hz | 1 kHz | 2 kHz | 4 kHz | 8 kHz |
| 30 | 30 | 25 | 35 | 30 | 45 | 20 | 35 | 30 |
| 30 | 50 | 65 | 30 | 35 | 30 | 50 | 36 | 35 |
| 65 | 83 | 90 | 75 | 43 | 35 | 25 | 40 | 50 |
| 10 | 10 | 10 | 10 | 10 | 10 | 10 | 10 | 10 |
Question 2: Part A
The composite sound reduction of two elements can be used using the weighted sound reduction index formula given below:
Where;
D = Level difference
S = Area of the test element through which the noise is transmitted
A = Total sound absorption by the element
Therefore, the composite sound reduction of the two elements can be determined by using the above formulae which can be used to the absorption factors of the two elements given by [ ]. With the absorption factors of the two elements and the average sound pressure of the source and receiving area, the composite sound reduction can be determined for the two elements.
Question 2: Part B
Using the explanation given above it is possible to show that the 10 dB rule works, i.e. “There is no benefit in increasing the sound reduction of the larger element more that 10 dB over the smaller element which has a lesser sound reduction.”
Let’s now consider the parameters of the two elements;
Element 1: Area = 9 m2 and Rw = 40 dB
Element 2: Area = 2 m2 and Rw = 30 dB
The composite sound reduction equation provided above can be used to proof that the 10 dB rule works, by computing the absorption factors for each element, which in the case of these two elements can be calculated from the given details of the two elements. The calculations for absorption factors for the two elements are shown below:
Element 1
Element 2
The above results for the absorption factors of both elements proves the 10 dB rule since their values are close despite the difference of 10 dB between the two elements.
Question 3: Part A
Sound Reduction is given by the formula shown below:
- Glass/windows
- Brick wall
- Spandrel panels
Question 3: Part B
The plot is shown below:
Question 4
Acoustics and sustainability are the two key considerations when designing sustainable or green buildings mainly because both are positively related in terms of the selected specifications, where those of one aspect of a building i.e. acoustics are dependent of the specifications of the building’s sustainability. This is highly attributable to the fact that, acoustics which are majorly concerned with sound insulation have become a very important factor when designing sustainable buildings as our environments continue to become noisier. The reason why acoustic has become a highly influential factor is because sound insulation has a significant impact on the extents of embodied energy in a particular building, which makes it essential to clearly understand the effect of sound insulation on embodied energy levels right from the beginning of the designing of sustainable buildings.
The close connection between acoustic (sound insulation) and sustainability is how the former influences the latter on basis of embodied energy, especially because embodied energy in a particular building can be effectively reduced by re-using an existing building through refurbishments that enables acoustic specifications are fulfilled in a manner that is very cost effective. This is in most cases achieved through timely up front acoustic testing of an existing building to understand its performance prior to refurbishment. Hence, upon establishing the acoustic performance of an existing building as well as understanding its restrictions and limitations, the sustainability of the building can be significantly improved by alleviating these restrictions or limitations.
When designing sustainable buildings, acoustics have become a very significant consideration because it determines the type of materials used in the construction of the sustainable building which is an indication of how the two components i.e. sustainability and acoustics are interrelated. Therefore, early acoustic testing is in most cases carried out as an effective an method to make sure that designs of sustainable buildings are sufficient, and that there is high quality construction in which sustainability is given priority. As a result, the architects usually make decisions of the construction materials to be used in a sustainable building either lightweight or heavyweight materials based of the intended quality of acoustics (sound insulation) as well as its subsequent sustainability. For instance, high/heavy weight materials are in most cases favored for enhanced acoustics; however lightweight materials such as timber often offer better or equal acoustic performance. This means that sustainability of buildings can be improved by using lightweight construction due to their less embodied energy compared to heavyweight construction materials apart from achieving higher levels of acoustic performance do not lead to desired sustainability.
Therefore, as it is theoretically know, a ±6 dB change in acoustic performance or sound insulation is equivalent to a doubling or halving of mass of construction materials for a particular building. This implies that, from the perspective of sustainability when acoustic parameters are over specified there will be an eventual significant impact on the created waste. This indicates that acoustic performance considerations or specifications or parameters in a particular building have a direct impact on its sustainability, hence necessitating the need to always make sure that a balance has been achieved between acoustic and sustainability at the design level of a building.
Furthermore, there are various products that are used for the enhancement of the acoustic of a vented façade. For instance, glass fiber reinforced concrete (GFRC) acoustic panels are one of the products often used in constructing vented facades for enhanced acoustic performance because they not only lead to sound insulation, but also improves sustainability of the building. Mineral wool is the other product used within partitions of vented facades for the purpose of acoustic dampening within stud walls, and it results to significant enhancement in acoustic performance in addition to being sustainable and cost effective method.
Question 5
A copy of the Excel spreadsheet is attached below:
When the absorptive panels are spread throughout the room more sound will be absorbed because they will be in proximity to the source of sound leading to significant sound reduction; however when they are placed in one big area there will be less sound reduction since they will be overlying each other.
Question 6
Where;
Lw = Sound power level 10-12 w(dB)
Lp = Sound pressure level 20 mPa (dB)
D= distance from fan in meters
dB
D = 25 meters
References
Fahy, F. and Gardonio, P. (2007), Sound and Structural Vibration: Radiation, Transmission and Response, (2nd edition). London: Academic Press.
Lohse, D., Schmitz, B. and Versluis, M. (2001), “Snapping shrimp make flashing bubbles”. Nature , Vol. 413 Issue: 6855, pp. 477–478.
Pohlmann, K. (2010), Principles of Digital Audio, (6th edition). New York, NY: McGraw Hill Professional. p. 336-339.
Raichel, D. R. (2006), The Science and Applications of Acoustics, (2nd edition). London: Springer.
Wilson, C. E. (2006), Noise Control, (Revised edition). Malabar, FL: Krieger Publishing Company.
We can write this or a similar paper for you! Simply fill the order form!
