Acoustics Basics

1 Friedrich Schönholtz, † Bad Hersfeld

Acoustic fundamentals I. Airbor Airborne ne soun sound d Basic physics 1. General

The human ear perceives sounds chiefly through the medium of the surrounding air. A sound source sets the air vibrating, causing a cycle of compression and expansion. Superimposed over normal air pressure, these oscillations propagate in the form of waves. Upon reaching the human ear, these sound waves cause our eardrums to vibrate, thus triggering the process of hearing. The greater the amount of air compression and expansion produced by a sound source, the louder the sound appears to our hearing. But the human ear not only perceives loudness. Some sound sources cause the air to compress and expand more often in unit time than others. The number of vibrations per second is referred to as the frequency of airborne sound, measured in Hertz (abbreviated to Hz). The greater the number of vibrations per second, the higher the „tone“ perceived by the human ear. Conversely, a lower frequency is heard as a lower tone. Fig. 1 shows a compression/expansion curve which is „higher“ than that in Fig. 2, i.e. it represents a louder sound. On the other hand, in Fig. 2 the airborne sound pressure vibra-

Acoustic fundamentals tions occur more often in a time interval „t“ than in Fig. 1, i.e. the sound has a higher tone. 2. Sound field parameters

These air vibrations can be measured and physically analyzed in terms of their key variables, referred to as „sound field parameters“. Some of these parameters are described below.

Fig. 2

2.1 Sound velocity

The sound velocity „c“ is the speed at which sound waves travel - about 333 m/s under normal conditions. 2.2 Sound pressure

The term „sound pressure“ refers to the alternate compression and expansion of air caused by a sound source. These pressure variations are measured in µbar (microbars).

d n u r o a s b n µ o i n s i s e e r r p u s m s o e r C p

Fig. 1

s e r p d n u o . s r a n b o µ i s n n i a e p r x u E s

Table of contents I. Airborne sound Basic physics 1. Gen Genera eral. l. . . . . . . . . . . . . . . . . . . . . . . 3.1 3.1 2. So Soun und d fie field ld par param amet eter ers s . . . . . . . . . . 3.1 3.1 2.1 Soun Sound d velocit velocity y . . . . . . . . . . . . . . . . . 3.1 3.1 2.2 Soun Sound d pressur pressure e . . . . . . . . . . . . . . . . 3.1 3.1 2.3 Sou Sound nd powe powerr . . . . . . . . . . . . . . . . . . 3.2 II. Sound pressure level and evaluation 1. Dec Decibe ibels ls . . . . . . . . . . . . . . . . . . . . . . 3.2 3.2 2. Oct Octave ave ban band. d. . . . . . . . . . . . . . . . . . . 3.2 3.2 3. One One-th -third ird oct octave ave ban band d . . . . . . . . . . . 3.3 3.3 4. Pho Phon. n. . . . . . . . . . . . . . . . . . . . . . . . . 3.3 3.3 5. A, B, C weig weighti hting ng . . . . . . . . . . . . . . . 3.4 3.4 6. Me Measu asurin ring-s g-surf urface ace sou sound nd pre pressu ssure re level . . . . . . . . . . . . . . . . . . . . . . . . . 3.5 III. Outdoor behaviour of sound 1. Sou Sound nd prop propaga agatio tion. n. . . . . . . . . . . . . . 3.6 2. Per Permis missib sible le valu values es . . . . . . . . . . . . . . 3.6 3.6 3. In Infl flue uenc nce e of di dist stan ance ce . . . . . . . . . . . . 3. 3.6 6 4. Le Lega gall immi immiss ssio ion n limi limits ts . . . . . . . . . . . 3.7 3.7 5. Behaviour of multiple sound sources . . 3.7 IV. Indoor sound pressure levels and weighting 1. Gen Genera eral. l. . . . . . . . . . . . . . . . . . . . . . . 3.8 3.8 2. Abs Absorp orptio tion n factor factor/ab /absor sorpti ption on surfa surface, ce, reverberation time . . . . . . . . . . . . . . 3.8 2.1 Abs Absorp orptio tion n faxt faxtor or  . . . . . . . . . . . . . . 3.8 2.2 Equi Equivalen valentt absorp absorption tion surf surface ace . . . . . 3.8 3.8 2.3 Me Mean an reverb reverbera eratio tion n time time T m (s) . . . . 3.8 3.8 3. Ev Evalu aluati ation/ on/wei weighe ghed d curve curves. s. . . . . . . . 3.9 3.9 3.1 Rel Relati ative ve sound sound pres pressur sure e level level . . . . . 3.9 3.9 3.2 Cumu Cumulativ lative e sound sound pressu pressure re level level . . 3.10 3.10 V. Sound power level 1. Gen Genera eral. l. . . . . . . . . . . . . . . . . . . . . . 3.1 3.10 0 2. Ov Over eral alll soun sound d powe powerr leve levell . . . . . . . 3.1 3.10 0 3. Re Rela lati tive ve so soun und d powe powerr leve levell . . . . . . 3. 3.11 11 4. So Soun und d po powe werr le leve vell L WA . . . . . . . . . . 3.11 5. Re Rela lati tion onsh ship ip bet betwe ween en sou sound nd pressure pres sure and sound sound power power level . . 3.11 VI. Sound attenuation by connected AHU ducting 1. Gen Genera eral. l. . . . . . . . . . . . . . . . . . . . . . 3.1 3.12 2 2. Da Damp mpin ing g by co conn nnec ecte ted d syst system em components . . . . . . . . . . . . . . . . . . 3.12 2.1 Stra Straight ight duct duct secti sections. ons. . . . . . . . . . . 3.12 2.2 Duct elbow sect sections ions . . . . . . . . . . . . 3.12 3.12 2.3 Ang Angula ularr defle deflect ctors ors . . . . . . . . . . . . . 3.13 3.13 2.4 Bran Branch ch fitting fittings. s. . . . . . . . . . . . . . . . . 3.13 3.13 2.5 Chan Changes ges in cros cross s section. section. . . . . . . . 3.14 2.6 Silen Silencers cers.. . . . . . . . . . . . . . . . . . . . . 3.14 3.14 2.7 Outl Outlet et reflec reflection tion . . . . . . . . . . . . . . . 3.14 VII. Conversion of sound power into sound pressure levels (indoors) 1. Gen Genera eral. l. . . . . . . . . . . . . . . . . . . . . . 3.1 3.15 5 2. Di Dire rect ctio iona nall fact factor or . . . . . . . . . . . . . . 3.1 3.15 5 3. Con Conver versio sion n . . . . . . . . . . . . . . . . . . . 3.16 3.16 4. Ev Evalu aluati ation. on. . . . . . . . . . . . . . . . . . . . 3.1 3.16 6 5. Ex Examp ample le . . . . . . . . . . . . . . . . . . . . . 3.1 3.16 6 VIII. Calcu Calculation lation examples examples 1. Ven Ventil tilati ation on of res reside identi ntial al units units.. . . . . 3.17 3.17 2. Ax Axial ial-fl -flow ow fan . . . . . . . . . . . . . . . . . 3.19 3.19 2.1 Soun Sound d press pressure ure leve levell inside inside the factory hall hall . . . . . . . . . . . . . . . . 3.19 3.19 2.2 Outd Outdoor oor soun sound d pressu pressure re level IX. Fans as sound sound sources - summary and addenda 1. Gen Genera eral. l. . . . . . . . . . . . . . . . . . . . . . 3.2 3.21 1 2. Ai Airb rbor orne ne noi noise se . . . . . . . . . . . . . . . . 3.2 3.21 1 3. Sou Sound nd emis emissio sion n . . . . . . . . . . . . . . . 3.24 3.24 4. St Struc ructur ture-b e-born orne e noise noise tran transm smiss ission ion / vibration insulation insulation . . . . . . . . . . . . . 3.25 3.25 X. Technical information in TLT catalogues cata logues . . . . . . . . . . . . . . . . . . . . 3.26

3

Acoustic fundamentals Sound pressure p is the root-meansquare value of pressure increase p+ caused by compression or pressure decrease p- caused by expansion of the ambient air, respectively.

3

2.3 Sound power

Sound power is a theoretical quantity which cannot be measured. It is calculated and expressed in watts (W). To illustrate the difference between sound pressure and sound power, let us consider the example of a trumpet player. What we hear coming out of the instrument are sound pressure waves that trigger the process of hearing via our eardrums. What we don’t hear is the amount of work done by the player to produce the sound, i.e. the „power“ input made by blowing into the mouthpiece. This power is necessary to generate the sound waves (reduced according to the trumpet’s efficiency); it is referred to as sound power or acoustic power.

As we move away from the trumpet player, his music appears to fade, i.e. decrease in loudness. In a room with a strong echo the instrument will sound differently than in a room decorated with heavy drapery and carpets. Thus, the sound pressure perceived by our ear is dependent on distance and space. But regardless of what we hear (i.e. of distance and space conditions), the trumpet player must expend the same amount of energy. In other words, sound power is not dependent on distance and space. This is what makes this parameter so valuable. As an objective

2 quantity that cannot be influenced, it constitues an excellent starting point for all acoustic calculations.

II. Sound pressure level and evaluation

Lp = 20 x log 1 = 20 x 0 = 0 dB If the measured sound pressure is equal to the pain threshold (200 µbar), the ratio is 200 µbar 0,0002 µbar

= 1.000.000

1. Decibels

Using this in our equation, we obtain

The human ear perceives sound pressure waves directly and evaluates them according to their strength and pitch. As far as loudness is concerned, we can perceive sounds down to a sound pressure of about 0,00002 µbar, a level referred to as the threshold pressure of audibility. Moreover, all human hearing takes place in the 20 - 20.000 Hz range. Lower (infrasonic) or higher (ultrasonic) sounds are inaudible for us. From a sound pressure of 200 µbar upwards, sound waves will produce a sensation of pain in an average human listener; this is referred to as the „threshold of pain“. A very broad interval (0.0002 to 200 µbar) thus separates the thresholds of audibility and pain, and to make this range more easily manageable arithmetically, a method has been adopted whereby the actually measured sound pressure is expressed in relation to the threshold pressure of audibility. Thus, it is said that a given sound has a pressure of, e.g., 10, 1.000 or 100.000 times the threshold pressure of audibility. To obtain smaller numbers, the ratio thus obtained is logarithmized. The value of the resulting logarithm is referred to as a the sound power level.

Lp = 20x lo log g 1. 1.00 000. 0.00 000 0 = 20x 6 = 12 120 0 dB

We can thus write the following equation: sound pressure in µbar Lp = 20 x log. measured threshold pressure of audibility in µbar

The unit in which the logarithmic term is expressed is „decibels“ (dB). At this point it appears pertinent to remember the following: log 1 = 0 log 10 = 1 log 100 = 2 etc. up to log 1.000.000 = 6 Thus, if the measured sound pressure is equal to the threshold pressure of audibility, the ratio becomes 1. According to the equation, we can write:

2. Octave band

Most sounds are composed of multiple tones having different frequencies. The effect can be likened to an orchestra, where many instruments and instrument types, from violin to bass drum, cooperate to produce one aggregate sound. For an analysis, it would be necessary to make each instrument play individually.

3

Acoustic fundamentals

Similarly, a sound composed of many tones, such as that emitted by a fan, can be analyzed and broken down into its individual frequency constituents. In practice this is done with the aid of microphones combined with suitable upstream filters so as to record only sound constituents („tones“) of a given frequency. These constituents are then measured.

3

7. 2.816 – 5.600 Hz Octave center frequency = 4000 Hz 8. 5.600 – 15.000 Hz Octave center frequency = 8000 Hz This method of sound measurement (i.e., analysis) yields the so-called sound pressure level. 3. One-third octave band

For this purpose, the frequency range from 20 - 15,000 Hz has been divided into 8 bands referred to as „octaves“. 1. 20 – 90 Hz Octave center frequency =

63 Hz

2. 90 – 179 Hz Octave center frequency =

125 Hz


250 Hz


500 Hz

5. 704 – 1.408 Hz Octave center frequency = 1000 Hz 6. 1.408 – 2.816 Hz Octave center frequency = 2000 Hz

The division of the 20 - 15,000 Hz frequency range into 8 octaves is too coarse for many purposes. A system has therefore been adopted whereby this range is broken down into 24 intervals, i.e. each octave is further divided by three. These intervals are called „one-third octaves“. Sound measurements in a one-third octave band give a more accurate evaluation of the acoustic situation. A still more precise evaluation of the sound range can be achieved with the aid of filters having bandwidths of 1/12th or even 1/24th of an octave. FFT analyzers can isolate bandwidths as narrow as 1 Hz with the aid of suitable filters.

4. Phon

The phon is a unit related to dB. It corresponds to the sound pressure level of a 1000 Hz tone in decibels. By comparing tones of other frequencies with 1.000 Hz tones, it has been found that different loudnesses (and hence, different sound pressures) are necessary at different frequencies to produce the same perceived loudness in a human ear.


4 Through extensive tests with large numbers of respondents it has been possible to establish curves of identical loudness. These reveal that to obtain a loudness perception identical to 50 dB at 1000 Hz, the following sound pressures are necessary at the stated frequencies:

3 Identical sound pressure – low fr equency (high tone)

63 Hz 125 Hz 2000 Hz 8000 Hz

Identical sound pressure – high frequency (high tone)

73 dB 66 dB 50 dB 62 dB

5. A, B, C weighting

Curves obtained by the above process have been simplified and processed into universally accepted „weighted“ curves covering three dB ranges: up to 60 dB 60 to 100 dB over 100 dB

curve A curve B curve C

dB 120

100

80

60 B d 40 n i e r u s 20 s e r p d n u 0 o S 20

50

100

500

1000 Frequency

5000

10 000

Hz

The above diagram shows curves of identical perceived loudness.

Bewertungstabelle: Weighting table

Octave center frequency

Oktavmittenfrequenz Weighting according to Bewertung nach curve

63

125

250

500

1000

2000

4000

8000

A

-26,1

-16,1

-8,6

-3,2

0

+1,2

+1,0

-1,1

B

-9,4

-4,3

-1,4

-0,3

0

-0,2

-0,8

-3,0

C

-0,8

-0,2

0

0

0

-0,2

-0,8

-3,0

Decibel curves are not strictly tied to their application range, i.e. it is possible to depart from the recommended range allocation by agreement and to use the same weighted curve for all sounds between 0 and 120 dB. In fact, it has recently been agreed to use the A-weighted curve for all noise measurements, i.e. to state the overall sound pressure level LPa in dB.

5 6. Measuring-surface sound pressure level

The measuring-surface sound pressure level ¯L is defined as the energetic mean1) of multiple sound level measurements over the measuring surface S, corrected to eliminate external noise and room influences (reflections) where applicable. LA is the corresponding A-weighted measuring-surface sound pressure level. The measuring surface S is an assumed area encompassing the soundemitting machine at a defined distance (usually 1 m). In construing this theoretical surface, it is deemed to be made up of simple surfaces or elements such as spheres, cylinders or squares generally following the exterior machine contour. Individual projecting elements which do not contribute in any major way to the emission of sound are not taken into account. Similarly, sound-reflecting enclosure surfaces such as floors or walls are not deemed to be part of the measuring surface. Measuring points should be sufficient in number and distributed evenly over the measuring surface. Their number depends on the size of the machine and on the uniformity of the sound field.

Acoustic fundamentals Since it is common in acoustics to work with logarithmic ratio quantities, the measuring surface area (in m 2) is related to a reference surface, and the resulting measuring-surface level LS is adopted as the characteristic parameter: LS = 10 lg

S S0

in dB

S = Measuring surface in m2 So = 1 m2 (Reference surface)

1) The mean value (determined over several points in space or time) of several sound levels measured on a given source is obtained using the following equation:

¯L = 10 lg (

1 n

i=n

·  10 0,1 Li ) i=1

If the difference between the individual levels is smaller than 6 dB, an approximate arithmetic mean can be obtained as follows:

¯L 

1 n

i=n

·  10 Li i=1

Measuring surface S

Measuring points distributed over the surface of S

3


6

III. Outdoor behaviour of sound 1. Sound propagation

The acoustic output emanating from the outlet side of a centrifugal roof3 mounted fan can propagate almost freely except where it is reflected by nearby building structures. A small portion of the sound waves will strike the roof surface and be reflected from it. Thus, in the absence of nearby buildings, and disregarding the negligible amount of reflection from the roof, the microphone in our drawing will record the sound pressure level directly emitted from the centrifugal roof-mounted fan. Such measurements can be used to assess the noise exposure of residents in the surrounding neighbourhoods. 2. Permissible values

In Germany, guide values for permissible sound pressure levels in specific neighbourhood types are given in the Technical Instruction for the Protection from Noise, abbreviated to „TALärm“. It stipulates that where no buildings lie within 3 m from the industrial site’s perimeter, measurements are to be conducted at a distance of 0.5 m from the open window most strongly affected by the noise. The following immission values are defined: a) for zones occupied exclusively by commercial-use and industrial facilities, as well as residential units for their proprietors, managers, supervisors and standby personnel: LPA = 70 dB b) for zones occupied predominantly by commercial-use facilities: daytime LPA = 65 dB nighttime LPA = 50 dB c) for zones occupied by commercial-use facilities and residential units, without predominance of either type: daytime LPA = 60 dB nighttime LPA = 45 dB d) for zones occupied predominantly by residential units: daytime LPA = 50 dB nighttime LPA = 35 dB

e) for zones occupied exclusively by residential units: daytime LPA = 45 dB nighttime LPA = 35 dB f) for sanatorium/spa areas, hospitals and medical care institutions: daytime LPA = 45 dB nighttime LPA = 35 dB g) for residential units structurally connected to the facility: daytime LPA = 40 dB nighttime LPA = 30 dB The nighttime is deemed to last 8 hours, commencing at 10:00 p.m. and ending at 6:00 a.m. It may be moved back or forward by one hour where required by special local circumstances or compelling operational reasons, provided that nearby residents remain assured of an 8 hours’ nightly rest [source: TA-Lärm]. 3. Influence of distance

A sound fades - i.e. its sound pressure level diminishes - with increasing distance from its source. Experience shows that once a certain distance from the source is exceeded, doubling the distance will reduce the sound pressure level by 5 dB. However, this decrease only takes place beyond the point where the sound field becomes uniformly and fully developed (i.e. homogeneous). In the case of roof-mounted fans, this point is located about 4 m from the source. Measurements have confirmed that the „5 dB law“ does not apply to measuring points situated closer to the fan.

Distance from roof-mounted fan 4 8 16

32

64

128 m

Decrease in sound pressure fan 0 5 10

15

20

25 dB

Actually, the decrease depends on the environment. Assuming a value of 5 dB will be correct in an average case; the theoretical value is 6 dB.

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Acoustic fundamentals Thus, where the legal immission limit is almost „exhausted“ already by other sound sources, any newly added equipment may have to be designed for sound levels far beyond the legal maximum.

4. Legal immission limits

Maximum immission levels are defined by legislators for each zone type. It must be noted in this context that the legal immission limit represents the total of all sound pressure levels incident at the measuring point, i.e. each facility and each component of an overall installation is itself allowed to account only for a fraction of the legal limit.

In this case, rather than imposing excessive noise protection demands on the new equipment, it may be practical to implement carefully chosen sound control measures on existing installations.

Moreover, since a noise protection measure omitted („forgotten“) at the planning stage will usually be extremely costly and difficult to implement retroactively, it is recommended to conduct acoustic calculations or, in the case of major projects, to commission an acoustic expert’s study at the earliest possible point of the planning process.

5. Behaviour of multiple sound sources If several sound sources (e.g. roof-mounted fans) of the same loudness are operating side by side, the overall sound pressure level will increase as follows:

Number of devices

2

3

4

5

6

8

10

15

20

30

Approx. level increase (dB) 3

5

6

7

8

9

10

12

13

15

With two roof-mounted fans of different loudness operating concurrently, the higher of their two sound pressure levels must be marked up as follows: Difference between higher and lower level (dB) 0

0,5

1,0

1,5

2,0

2,5

3,0

3,5

4,0

4,5

5,0

Level to be added (dB)

3,0

2,8

2,5

2,3

2,1

1,9

1,8

1,6

1,5

1,3

1,2

Difference between higher and lower level (dB)

5,5

6,0

6,5

7,0

7,5

8,0

9,0

10,0

11,0

13,0

15,0

20

Level to be added (dB)

1,1

1,0

0,9

0,8

0,7

0,6

0,5

0,4

0,3

0,2

0,1

0

Example:

Multiple centrifugal roof-mounting fans in service on the same roof. The noise pressure level at the reference point is to be determined: DRH 400/30 – 6 at 4 m: 60 dB DRV 500/30 – 6 at 4 m: 62 dB DRH 630/25 – 6 at 4 m: 68 dB Assuming a 5 dB level decrease with every doubling of the distance, we obtain: DRH 400/30 – 6 at 65 m: 40 dB DRV 500/30 – 6 at 64 m: 42 dB DRH 630/25 – 6 at 65 m: 48 dB Addition of the levels: 42 – 40 = 2 dB Level increase by 2,1 dB DRH 400/30 – 6 and DRV 500/30 – 6 together: 44,1 48 – 44,1 = 3,9 Level increase by 1,5 dB DRH 400/30 – 6 and DRV 500/30 – 6 and DRH 630/25 – 6 together: 48 + 1,5 = 49,5 The sound pressure level L PA at reference point 1 is approx. 50 dB. Noise pressure levels taken from the catalogue „Roof-Units“ Centrifugal, TLT-Turbo GmbH, Bad Hersfeld

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Acoustic fundamentals IV. Indoor sound pressure level and weighting 1. General

While sound can normally propagate 3 freely in outdoor environments, the indoor situation is quite different. Sound pressure waves emitted by a source into the room will strike the walls where they are in part absorbed (swallowed up) and in part reflected (thrown back). A person exposed to a sound source in a room will thus perceive both directly transmitted sound pressure waves and waves reflected from the walls.

8 It follows that sounds heard by the human ear in a room are subject to numerous influences. Apart from the location of the source in the room and the listener’s position relative to it, the size of the room and the acoustic properties of the walls (i.e. their ability to absorb and reflect sound waves) play important roles. A sound pressure value stated for an indoor location, e.g. in dB, will therefore be of little value unless it is accompanied by a detailed acoustical description of the room in question. Even where a sound pressure value is given in conjunction with an acoustical description (plus a description of the measuring point), it will only ap-

ply to this room and that specific point. It cannot be applied by extension to any other room having different acoustic properties. 2. Absorption factor/absorption surface/reverberation time

The acoustical properties of a room are described in terms of three parameters: 2.1 Absorption factor α

The surface of a wall fully absorbing all impinging sound waves would have an absorption factor α = 1. Since no existing wall can absorb all incoming sound, absorption capability is expressed in relation to that of a theoretical wall having an ideal absorption behaviour. In pratice, α rates between 0.02 and 0.4 are attained. Specific values are compiled in collections of tables. Some average absorption rates are given below. Room

m

Normal factory hall

0,02 – 0,07

Kitchen

0,03 – 0,08

Restaurant

0,05 – 0,1

Schools

0,07 – 0,1

Assembly halls

0,08 – 0,12

Offices

0,12 – 0,15

Studios

0,3 – 0,4

2.2 Equivalent absorption surface

The interior surface of a room is assumed to consist of completely reflective and completely absorptive surfaces. The portion of completely absorptive surfaces is referred to as the equivalent absorption surface A, expressed in m2 sabin. It is calculated using the equation A = αm x Fi (m2 sabin), where Fi is the interior room surface area expressed in m2. If the volume of the room is known, we can use the diagram plus the αm value from the above list to determine the absorption surface.

n i b a s



2

m A n o i t p r o s b A



2.3 Mean reverberation time Tm (s). Room volume V m3

This parameter is defined as the time interval during which the reverberati-

9 on of a sound diminishes by 60 dB. Acoustically „hard“ rooms with highly reflective walls (concrete, glass) have a longer reverberation time than their acoustically „soft“ counterparts (e.g. rooms furnished with drapes, soundabsorbing walls). Wallace Sabine found a relation between the equivalent absorption surface A and the reverberation time T. It can be expressed thus: A = 0,164 x V/Tm (m2 sabin) mit V = Volume of the room in m3.

Acoustic fundamentals 1000 500 n i b a s



3

2

m100



A 50 n o i t p r o s b A

10 5

Since the reverberation time can be measured, Sabine’s formula enables us to calculate the equivalent absorption surface directly.

25

50

100

250

500

1000

2500

5000

Room volume V m3

3. Evaluation/weighted curves NC curves

3.1 Relative sound pressure level

To establish an evaluation basis for sound and noise, scientists have defined various final loudness levels. It is stipulated that the actual (relative) sound pressure level in a room, determined at a given measuring point, shall not be higher in any frequency range than the agreed weighting curve. Different weighted curves exist, e.g. NC curve DIN phon curve ISO curve

80 70 

B d l e v e l e r u s s e r p d n u o S

60



50 40 30 20 15 63

All of these curves are numerically dimensioned; the higher the number, the louder the sound is allowed to be.

125

250

500

1000

2000

4000

2000

4000

Octave center frequency Hz

Curves are shown in graphic form on the right of this page.

DIN phon curves 70 


60



50 40 30 20 15 63

125

250

500

1000

Octave center frequency Hz


10

3.2 Cumulative sound pressure level

Naturally, the relative sound pressure level in a room can be evaluated, e.g. according to curve A (refer to section 3 II). By logarithmic addition, we obtain the cumulative sound pressure level in dB(A) as outlined above.

ISO N curves 80 70 




60 50 40 30 20 15 63

125

250

500

1000

2000

4000

Octave center frequency Hz DIN phon curves 80 70 




Example: Relative sound pressure level measured in a real-life application, superimposed over the diagram of ISO N-curves.

V. Sound power level 1. General

As we have seen from the discussion of sound pressure waves in a room, reflection and absorption effects present a complicated picture. Managing these acoustic phenomena involves complicated calculations. The complexity, if not impossibility, of such calculations for a fan connected to an intake-side duct can easily be imagined. Such analyses can therefore not be conducted on the basis of the sound pressure level. An independent quantity is needed which is not influenced by position, the room, reflec-

60 50 40 30 20 15 63

125

250 500 1000 Octave center frequency Hz

tions and distances. We possess such a parameter in the form of sound power, expressed in watts (W). 2. Overall sound power level

As with the sound pressure, a lower limit (N0=10-12 watts) of sound power has been defined as a reference to which all actual sound power data are related. The resulting ratio is again logarithmized, as in the case of the sound pressure, according to the equation LW = 10 x log N/N0 (dB). The result is again expressed in decibels. It should be borne in mind that

2000

4000

this unit can thus denote both sound pressure and sound power. The overall cumulated sound power emitted by a source, compared with a defined threshold and logarithmized as above, is referred to as the overall sound power level. This variable represents our objective starting point for all further calculations.

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3. Relative sound power level

Since, as we shall see, all calculations must be performed as a function of frequency, it is necessary to know which sound constituents make up the overall sound power level. The result of this analysis is called the frequency response of the overall sound power level, or relative sound power level. By way of example, let us consider the fan DRV 400/30-4 listed on page 49 of TLT Turbo GmbH’s catalogue of centrifugal roof units. Its overall sound power level LWtot is specified as 95 dB (above roof level). We can thus derive the following relative sound power levels LWrel at the frequencies stated: 63 Hz:95 dB – 11,9 dB = 83,1 dB 125 Hz:95 dB – 4,9 dB = 90,1 dB 250 Hz:95 dB – 7,3 dB = 87,7 dB 500 Hz:95 dB – 8,2 dB = 86,8 dB 1000 Hz:95 dB – 9,2 dB = 85,8 dB 2000 Hz:95 dB – 13,9 dB = 81,1 dB 4000 Hz:95 dB – 12,6 dB = 82,4 dB 8000 Hz:95 dB – 11,8 dB = 83,2 dB 4. Weighted sound power level LWA

By carrying out the evaluation explained for the sound pressure level, using the A-weighted curve, we obtain the weighted sound power level LWA from the sound power level LW. 5. Relationship between sound pressure and sound power levels

Unlike sound pressure p, sound power W is not measured directly but calculated from sound pressure p, particle velocity n (alternating velocity of the molecules of the medium), and measuring surface S. W=p··S p

where  = q · c with = air density c = sound velocity in air becomes: 

p2

W = q · c · S

Assuming that both and c are constant, we obtain the following proportionality law: 

W ~ p2 · S Expressed in level terms, this yields an equation which plays an important role in all practical calculations: S

LW  ¯L + 10 lg S = ¯L + LS in dB 0 or rather, LWA  ¯LA + 10 lg SS = ¯LA + LS in dB 0 In other words, sound power level LW can be approximated as the sum of measuring surface sound pressure level ¯L and measuring surface level LS. From this relationship it can be concluded that for a given sound power level, assuming spherical or hemispherical sound propagation into free space (ideal sound propagation), the sound pressure level decreases by 6 dB when the distance from the source is doubled. This value may increase due to sound absorption by the air or floor, or diminish due to reflection from obstacles. Moreover, the decrease in sound pressure level may be amplified or attenuated by weather influences.

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VI. Sound attenuation by connected AHU ducting 1. General

A duct system connected to a fan will diminish its acoustic output, but the 3 sound-attenuating effects of the individual system components vary widely. For calculation purposes, one starts by determining the relative sound power level of the fan, then deducts the level difference resulting from attenuation by system component, taking into account the individual frequencies. 2. Damping by connected system components 2.1 Straight duct sections

Sheetmetal ducts have a minimal damping influence. For improved attenuation it would be necessary to line the duct with insulating material (e.g., rock wool matting) on its aircarrying side. For straightforward sheetmetal ducts without insulating lining, the damping effect per meter of ducting can be summarized thus:

] m / B d [ e c n e r e f f i d l e v e L

Octave center frequency [Hz]

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2.2 Duct elbow section

A duct elbow affording favourable flow conditions has a slight attenuating effect on high frequencies, but low frequencies (long waves) are transmitted virtually unchanged.

2


1

d=1,0m 0 63

125

d=0,5m 250


d=0,25m 500

d=0,1m 1000

2000

4000

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2.3 Angular deflector

An angular deflector providing unfavourable flow conditions has a more pronounced sound-damping effect, although again, mainly high frequencies are reduced.

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2.4 Branch fittings

In a Y-fitting, sound energy is split in the ratio of the outgoing duct cross sections.


Ratio of cross-sections

Acoustics Basics

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