1 Acoustic Fundamentals

1 Acoustic fundamentals

Friedrich Schönholtz, † tions occur more often in a time inter- Table of contents Bad Hersfeld val „t“ than in Fig. 1, i.e. the sound has a higher tone. I. Airborne sound Acoustic fundamentals Basic physics 2. Sound field parameters 1. General...... 3.1 I. Airborne sound 2. Sound field parameters ...... 3.1 These air vibrations can be measured 2.1 Sound velocity ...... 3.1 Basic physics 2.2 Sound pressure ...... 3.1 and physically analyzed in terms of 2.3 Sound power ...... 3.2 3 1. General their key variables, referred to as II. Sound pressure level and evaluation „sound field parameters“. Some of 1. Decibels ...... 3.2 The human ear perceives sounds these parameters are described be- 2. Octave band...... 3.2 chiefly through the medium of the sur- 3. One-third octave band ...... 3.3 low. 4. Phon...... 3.3 rounding air. A sound source sets the 5. A, B, C weighting ...... 3.4 air vibrating, causing a cycle of com- 6. Measuring-surface sound pressure pression and expansion. Superimpo- level ...... 3.5 sed over normal air pressure, these III. Outdoor behaviour of sound 1. Sound propagation...... 3.6 oscillations propagate in the form of 2. Permissible values ...... 3.6 waves. Upon reaching the human 3. Influence of distance ...... 3.6 ear, these sound waves cause our 4. Legal immission limits ...... 3.7 5. Behaviour of multiple sound sources. . 3.7 eardrums to vibrate, thus triggering IV. Indoor sound pressure levels and the process of hearing. weighting 1. General...... 3.8 The greater the amount of air com- 2. Absorption factor/absorption surface, pression and expansion produced by reverberation time ...... 3.8 2.1 Absorption faxtor ␣...... 3.8 a sound source, the louder the sound 2.2 Equivalent absorption surface . . . . . 3.8 appears to our hearing. But the hu- 2.3 Mean reverberation time Tm (s) . . . . 3.8 man ear not only perceives loudness. 3. Evaluation/weighed curves...... 3.9 3.1 Relative sound pressure level . . . . . 3.9 Some sound sources cause the air to 3.2 Cumulative sound pressure level . . 3.10 Fig. 2 compress and expand more often in V. Sound power level unit time than others. The number of 1. General...... 3.10 vibrations per second is referred to as 2. Overall sound power level ...... 3.10 the frequency of airborne sound, 3. Relative sound power level ...... 3.11 4. Sound power level LWA ...... 3.11 measured in Hertz (abbreviated to 2.1 Sound velocity 5. Relationship between sound Hz). The greater the number of vibra- pressure and sound power level . . 3.11 tions per second, the higher the ãto- The sound velocity „c“ is the speed at VI. Sound attenuation by connected AHU which sound waves travel - about 333 ducting ne“ perceived by the human ear. Con- 1. General...... 3.12 versely, a lower frequency is heard as m/s under normal conditions. 2. Damping by connected system a lower tone. components ...... 3.12 2.2 Sound pressure 2.1 Straight duct sections...... 3.12 Fig. 1 shows a compression/expansi- 2.2 Duct elbow sections ...... 3.12 The term „sound pressure“ refers to 2.3 Angular deflectors ...... 3.13 on curve which is „higher“ than that in the alternate compression and ex- 2.4 Branch fittings...... 3.13 Fig. 2, i.e. it represents a louder 2.5 Changes in cross section ...... 3.14 pansion of air caused by a sound 2.6 Silencers...... 3.14 sound. On the other hand, in Fig. 2 source. These pressure variations 2.7 Outlet reflection ...... 3.14 the airborne sound pressure vibra- are measured in µbar (microbars). VII. Conversion of sound power into sound pressure levels (indoors) 1. General...... 3.15 2. Directional factor ...... 3.15 3. Conversion ...... 3.16 4. Evaluation...... 3.16 5. Example ...... 3.16 VIII. Calculation examples 1. Ventilation of residential units. . . . . 3.17 2. Axial-flow fan ...... 3.19 2.1 Sound pressure level inside the factory hall ...... 3.19 2.2 Outdoor sound pressure level Compression sound pressure in µbar IX. Fans as sound sources - summary and addenda 1. General...... 3.21 2. Airborne noise ...... 3.21 3. Sound emission ...... 3.24 4. Structure-borne noise transmission / vibration insulation ...... 3.25 X. Technical information in TLT catalogues ...... 3.26 Fig. 1 Expansion sound pressure in µbar. Acoustic fundamentals 2

Sound pressure p is the root-mean- quantity that cannot be influenced, it Lp = 20 x log 1 = 20 x 0 = 0 dB square value of pressure increase p+ constitues an excellent starting point caused by compression or pressure for all acoustic calculations. If the measured sound pressure is equal to the pain threshold (200 decrease p- caused by expansion of the ambient air, respectively. II. Sound pressure level and µbar), the ratio is 200 µbar evaluation = 1.000.000 2.3 Sound power 0,0002 µbar 3 1. Decibels Sound power is a theoretical quantity Using this in our equation, we obtain which cannot be measured. It is cal- The human ear perceives sound Lp = 20 x log 1.000.000 = 20 x 6 = 120 dB culated and expressed in watts (W). pressure waves directly and evalua- To illustrate the difference between tes them according to their strength 2. Octave band and pitch. As far as loudness is con- sound pressure and sound power, let Most sounds are composed of multi- cerned, we can perceive sounds us consider the example of a trumpet ple tones having different frequen- down to a sound pressure of about player. cies. The effect can be likened to an 0,00002 µbar, a level referred to as orchestra, where many instruments What we hear coming out of the in- the threshold pressure of audibility. and instrument types, from violin to strument are sound pressure waves Moreover, all human hearing takes bass drum, cooperate to produce one that trigger the process of hearing via place in the 20 - 20.000 Hz range. Lo- aggregate sound. our eardrums. What we don’t hear is wer (infrasonic) or higher (ultrasonic) the amount of work done by the play- sounds are inaudible for us. From a For an analysis, it would be neces- er to produce the sound, i.e. the ãpo- sound pressure of 200 µbar upwards, sary to make each instrument play in- wer“ input made by blowing into the sound waves will produce a sensation dividually. mouthpiece. This power is necessary of pain in an average human listener; to generate the sound waves (redu- this is referred to as the ãthreshold of ced according to the trumpet’s effi- pain“. A very broad interval (0.0002 to ciency); it is referred to as sound po- 200 µbar) thus separates the thres- wer or acoustic power. holds of audibility and pain, and to make this range more easily manage- able 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. We can thus write the following equation: As we move away from the trumpet measured sound pressure in µbar player, his music appears to fade, i.e. Lp = 20 x log. threshold pressure of audibility in µbar decrease in loudness. In a room with The unit in which the logarithmic term a strong echo the instrument will is expressed is „decibels“ (dB). sound differently than in a room de- corated with heavy drapery and car- At this point it appears pertinent to pets. Thus, the sound pressure per- remember the following: ceived by our ear is dependent on di- log 1 = 0 stance and space. But regardless of log 10 = 1 what we hear (i.e. of distance and log 100 = 2 space conditions), the trumpet player etc. up to must expend the same amount of log 1.000.000 = 6 energy. In other words, sound power is not dependent on distance and Thus, if the measured sound pressu- space. This is what makes this para- re is equal to the threshold pressure meter so valuable. As an objective of audibility, the ratio becomes 1. Ac- cording to the equation, we can write: 3 Acoustic fundamentals

Similarly, a sound composed of many tones, such as that emitted by a fan, can be analyzed and broken down in- to its individual frequency constituents. In practice this is done with the aid of microphones combined with suitable upstream filters so as to re- 3 cord only sound constituents (ãto- nes“) of a given frequency. These constituents are then measured.

7. 2.816 Ð 5.600 Hz 4. Phon Octave center frequency = 4000 Hz The phon is a unit related to dB. It cor- 8. 5.600 Ð 15.000 Hz responds to the sound pressure level Octave center frequency = 8000 Hz of a 1000 Hz tone in decibels. By comparing tones of other frequencies This method of sound measurement with 1.000 Hz tones, it has been (i.e., analysis) yields the so-called found that different loudnesses (and sound pressure level. hence, different sound pressures) are 3. One-third octave band necessary at different frequencies to produce the same perceived loud- The division of the 20 - 15,000 Hz fre- ness in a human ear. quency range into 8 octaves is too co- arse for many purposes. A system has therefore been adopted whereby For this purpose, the frequency range this range is broken down into 24 in- from 20 - 15,000 Hz has been divided tervals, i.e. each octave is further di- into 8 bands referred to as „octaves“. vided by three. These intervals are 1. 20 Ð 90 Hz called „one-third octaves“. Sound Octave center frequency = 63 Hz measurements in a one-third octave band give a more accurate evaluation 2. 90 Ð 179 Hz of the acoustic situation. Octave center frequency = 125 Hz A still more precise evaluation of the 3. 176 Ð 352 Hz sound range can be achieved with the Octave center frequency = 250 Hz aid of filters having bandwidths of 1/12th or even 1/24th of an octave. 4. 352 Ð 704 Hz FFT analyzers can isolate band- Octave center frequency = 500 Hz widths as narrow as 1 Hz with the aid 5. 704 Ð 1.408 Hz of suitable filters. Octave center frequency = 1000 Hz 6. 1.408 Ð 2.816 Hz Octave center frequency = 2000 Hz Acoustic fundamentals 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 ne- 3 cessary at the stated frequencies: 63 Hz 73 dB Identical sound pressure Ð low frequency Identical sound pressure Ð high frequency 125 Hz 66 dB (high tone) (high tone) 2000 Hz 50 dB 8000 Hz 62 dB

5. A, B, C weighting Curves obtained by the above process have been simplified and pro- cessed into universally accepted „weighted“ curves covering three dB ranges: up to 60 dB curve A 60 to 100 dB curve B over 100 dB curve C dB

120

100

0 Sound pressure in dB

20 50 100 500 1000 Frequency 5000 10 000 Hz

The above diagram shows curves of identical perceived loudness.

Decibel curves are not strictly tied to their application range, i.e. it is possi- Bewertungstabelle:Weighting table Octave center frequency ble to depart from the recommended Oktavmittenfrequenz range allocation by agreement and to Weighting according to Bewertungcurve nach 63 125 250 500 1000 2000 4000 8000 use the same weighted curve for all sounds between 0 and 120 dB. In A -26,1 -16,1 -8,6 -3,2 Ϯ0 +1,2 +1,0 -1,1 fact, it has recently been agreed to B -9,4 -4,3 -1,4 -0,3 Ϯ0 -0,2 -0,8 -3,0 use the A-weighted curve for all noise measurements, i.e. to state the over- C -0,8 -0,2 Ϯ0 Ϯ0 Ϯ0 -0,2 -0,8 -3,0 all sound pressure level LPa in dB. 5 Acoustic fundamentals

6. Measuring-surface sound pres- Since it is common in acoustics to sure level work with logarithmic ratio quantities, the measuring surface area (in m2) is The measuring-surface sound pres- related to a reference surface, and ø sure level L is defined as the energe- the resulting measuring-surface level tic mean1) of multiple sound level LS is adopted as the characteristic pa- measurements over the measuring rameter: surface S, corrected to eliminate ex- 3 S ternal noise and room influences (re- LS = 10 lg in dB S0 flections) where applicable. LA is the 2 corresponding A-weighted measu- S = Measuring surface in m ring-surface sound pressure level. So = 1 m2 (Reference surface) The measuring surface S is an assu- med area encompassing the sound- 1) The mean value (determined over several points in space emitting machine at a defined di- or time) of several sound levels measured on a given sour- stance (usually 1 m). In construing ce is obtained using the following equation: this theoretical surface, it is deemed to be made up of simple surfaces or i = n ø 1 ⌺ 0,1 L L = 10 lg ( á 10 i ) elements such as spheres, cylinders n i = 1 or squares generally following the ex- terior machine contour. Individual If the difference between the individual levels is smaller than projecting elements which do not con- 6 dB, an approximate arithmetic mean can be obtained as fol- tribute in any major way to the emis- lows: sion of sound are not taken into ac- i = n ø 1 ⌺ count. Similarly, sound-reflecting en- L n á 10 Li closure surfaces such as floors or i = 1 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.

Measuring surface S

Measuring points distributed over the surface of S Acoustic fundamentals 6

III. Outdoor behaviour of sound 1. Sound propagation The acoustic output emanating from the outlet side of a centrifugal roof- 3 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 negli- gible amount of reflection from the ro- e) for zones occupied exclusively by Distance from of, the microphone in our drawing will residential units: roof-mounted record the sound pressure level di- daytime LPA = 45 dB fan 4 8 16 32 64 128 m rectly emitted from the centrifugal ro- nighttime L = 35 dB of-mounted fan. Such measurements PA Decrease in can be used to assess the noise ex- sound pressure posure of residents in the surrounding f) for sanatorium/spa areas, hospi- fan 0 5 10 15 20 25 dB neighbourhoods. tals and medical care institutions: daytime LPA = 45 dB Actually, the decrease depends on 2. Permissible values nighttime LPA = 35 dB the environment. Assuming a value of 5 dB will be correct in an In Germany, guide values for permis- average case; the theoretical value sible sound pressure levels in specific g) for residential units structurally is 6 dB. neighbourhood types are given in the connected to the facility: Technical Instruction for the Protec- daytime LPA = 40 dB tion from Noise, abbreviated to ãTA- nighttime LPA = 30 dB Lärm“. It stipulates that where no buildings lie within 3 m from the industri- The nighttime is deemed to last 8 al site’s perimeter, measurements hours, commencing at 10:00 p.m. and are to be conducted at a distance of ending at 6:00 a.m. It may be moved 0.5 m from the open window most back or forward by one hour where strongly affected by the noise. The required by special local circum- following immission values are defi- stances or compelling operational ned: reasons, provided that nearby residents remain assured of an 8 hours’ a) for zones occupied exclusively by nightly rest [source: TA-Lärm]. commercial-use and industrial facilities, as well as residential units for their proprietors, mana- 3. Influence of distance gers, supervisors and standby

personnel: LPA = 70 dB A sound fades - i.e. its sound pressure level diminishes - with increasing b) for zones occupied predominantly distance from its source. Experience by commercial-use facilities: shows that once a certain distance daytime LPA = 65 dB from the source is exceeded, doub- nighttime LPA = 50 dB ling the distance will reduce the c) for zones occupied by commerci- sound pressure level by 5 dB. Howe- al-use facilities and residential ver, this decrease only takes place units, without predominance of beyond the point where the sound either type: field becomes uniformly and fully de- veloped (i.e. homogeneous). In the daytime LPA = 60 dB case of roof-mounted fans, this point nighttime LPA = 45 dB is located about 4 m from the source. d) for zones occupied predominantly Measurements have confirmed that by residential units: the „5 dB law“ does not apply to mea-

daytime LPA = 50 dB suring points situated closer to the nighttime LPA = 35 dB fan. 7 Acoustic fundamentals

4. Legal immission limits Thus, where the legal immission limit Moreover, since a noise protection is almost „exhausted“ already by measure omitted („forgotten“) at the Maximum immission levels are defi- other sound sources, any newly ad- planning stage will usually be extre- ned by legislators for each zone type. ded equipment may have to be desi- mely costly and difficult to implement It must be noted in this context that gned for sound levels far beyond the retroactively, it is recommended to the legal immission limit represents legal maximum. conduct acoustic calculations or, in the total of all sound pressure levels the case of major projects, to com- 3 incident at the measuring point, i.e. In this case, rather than imposing ex- mission an acoustic expert’s study at each facility and each component of cessive noise protection demands on the earliest possible point of the plan- an overall installation is itself allowed the new equipment, it may be prac- ning process. to account only for a fraction of the le- tical to implement carefully chosen gal limit. sound control measures on existing installations. 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 Multiple centrifugal roof-mounting fans in ser- Example: vice on the same roof. The noise pressure level at the reference point is to be determined: DRH 400/30 Ð 6 at 4 m: 60 dB DRV 500/30 Ð 6 at 4 m: 62 dB DRH 630/25 Ð 6 at 4 m: 68 dB

Assuming a 5 dB level decrease with every doubling of the distance, we obtain: DRH 400/30 Ð 6 at 65 m: 40 dB DRV 500/30 Ð 6 at 64 m: 42 dB DRH 630/25 Ð 6 at 65 m: 48 dB

Addition of the levels: 42 Ð 40 = 2 dB Level increase by 2,1 dB DRH 400/30 Ð 6 and DRV 500/30 Ð 6 together: 44,1 48 Ð 44,1 = 3,9 Level increase by 1,5 dB DRH 400/30 Ð 6 and DRV 500/30 Ð 6 and DRH 630/25 Ð 6 together: 48 + 1,5 = 49,5 The sound pressure level LPA at reference point 1 is approx. 50 dB.

Noise pressure levels taken from the catalogue „Roof-Units“ Centrifugal, TLT-Turbo GmbH, Bad Hersfeld Acoustic fundamentals 8

IV. Indoor sound pressure It follows that sounds heard by the hu- ply to this room and that specific level and weighting man ear in a room are subject to nu- point. It cannot be applied by extensi- merous influences. Apart from the lo- on to any other room having different 1. General cation of the source in the room and acoustic properties. the listener’s position relative to it, the size of the room and the acoustic pro- 2. Absorption factor/absorption While sound can normally propagate surface/reverberation time 3 freely in outdoor environments, the in- perties of the walls (i.e. their ability to door situation is quite different. Sound absorb and reflect sound waves) play The acoustical properties of a room pressure waves emitted by a source important roles. are described in terms of three para- into the room will strike the walls whe- meters: A sound pressure value stated for an re they are in part absorbed (swallo- α wed up) and in part reflected (thrown indoor location, e.g. in dB, will there- 2.1 Absorption factor back). fore be of little value unless it is ac- The surface of a wall fully absorbing companied by a detailed acoustical all impinging sound waves would ha- A person exposed to a sound source description of the room in question. ve an absorption factor α = 1. Since in a room will thus perceive both di- Even where a sound pressure value no existing wall can absorb all inco- rectly transmitted sound pressure wa- is given in conjunction with an acou- ming sound, absorption capability is ves and waves reflected from the stical description (plus a description expressed in relation to that of a theo- walls. of the measuring point), it will only ap- retical wall having an ideal absorption behaviour. In pratice, α rates between 0.02 and 0.4 are attained. Spe- cific values are compiled in collec- tions of tables. Some average absorption rates are given below. ␣ Room m Normal factory hall 0,02 Ð 0,07 Kitchen 0,03 Ð 0,08 Restaurant 0,05 Ð 0,1 Schools 0,07 Ð 0,1 Assembly halls 0,08 Ð 0,12 Offices 0,12 Ð 0,15 Studios 0,3 Ð 0,4

2.2 Equivalent absorption surface The interior surface of a room is as- sumed 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 α 2 using the equation A = m x Fi (m sabin), where Fi is the interior room surface area expressed in m2. If the vo- sabin

2 lume of the room is known, we can m α use the diagram plus the m value from the above list to determine the absorption surface.

2.3 Mean reverberation time Tm (s). Absorption A This parameter is defined as the time Room volume V m3 interval during which the reverberati- 9 Acoustic fundamentals on of a sound diminishes by 60 dB. Acoustically „hard“ rooms with highly 1000 reflective walls (concrete, glass) have 500 a longer reverberation time than their acoustically „soft“ counterparts (e.g. rooms furnished with drapes, sound- absorbing walls). Wallace Sabine sabin 3 found a relation between the equiva- 2 100 m lent absorption surface A and the re- 50 verberation time T. It can be expressed thus: A = 0,164 x V/Tm (m2 sabin) Absorption A mit V = Volume of the room in m3. 10 Since the reverberation time can be 5 measured, Sabine’s formula enables 25 50 100 250 500 1000 2500 5000 us to calculate the equivalent absorp- 3 tion surface directly. Room volume V m 3. Evaluation/weighted curves 3.1 Relative sound pressure level NC curves 80 To establish an evaluation basis for sound and noise, scientists have defi- 70 ned various final loudness levels. It is stipulated that the actual (relative) 60 dB sound pressure level in a room, determined at a given measuring point, shall not be higher in any frequency 50 range than the agreed weighting curve. 40 Different weighted curves exist, e.g. 30

NC curve Sound pressure level DIN phon curve ISO curve 20 15 All of these curves are numerically di- 63 125 250 500 1000 2000 4000 mensioned; the higher the number, the louder the sound is allowed to be. Octave center frequency Hz Curves are shown in graphic form on the right of this page. DIN phon curves 70

60 dB

30 Sound pressure level

20 15 63 125 250 500 1000 2000 4000

Octave center frequency Hz Acoustic fundamentals 10

3.2 Cumulative sound pressure ISO N curves level 80

Naturally, the relative sound pressure 70 level in a room can be evaluated, e.g.

according to curve A (refer to section

dB 60 3 II). By logarithmic addition, we obtain the cumulative sound pressure level in dB(A) as outlined above. 50

30 Sound pressure level

20 15 63 125 250 500 1000 2000 4000

Octave center frequency Hz

DIN phon curves 80

dB 60

30 Sound pressure level

Example: Relative sound pressure le- 20 vel measured in a real-life application, 15 superimposed over the diagram of 63 125 250 500 1000 2000 4000 ISO N-curves. Octave center frequency Hz

V. Sound power level tions and distances. We possess this unit can thus denote both sound such a parameter in the form of sound pressure and sound power. 1. General power, expressed in watts (W). The overall cumulated sound power As we have seen from the discussion 2. Overall sound power level emitted by a source, compared with a of sound pressure waves in a room, defined threshold and logarithmized reflection and absorption effects pre- As with the sound pressure, a lower li- as above, is referred to as the overall mit (N =10-12 watts) of sound power sent a complicated picture. Managing 0 sound power level. This variable re- these acoustic phenomena involves has been defined as a reference to presents our objective starting point complicated calculations. The com- which all actual sound power data are for all further calculations. plexity, if not impossibility, of such related. The resulting ratio is again lo- calculations for a fan connected to an garithmized, as in the case of the intake-side duct can easily be imagi- sound pressure, according to the ned. Such analyses can therefore not equation LW = 10 x log N/N0 (dB). be conducted on the basis of the so- The result is again expressed in deci- und pressure level. An independent bels. It should be borne in mind that quantity is needed which is not influenced by position, the room, reflec-

11 Acoustic fundamentals 3. Relative sound power level Assuming that both ␦ and c are con- stant, we obtain the following propor- Since, as we shall see, all calculati- tionality law: ons must be performed as a function of frequency, it is necessary to know W ~ p2 á S which sound constituents make up the overall sound power level. The re- Expressed in level terms, this yields sult of this analysis is called the fre- an equation which plays an important 3 quency response of the overall sound role in all practical calculations: power level, or relative sound power ø S ø LW L + 10 lg S = L + LS in dB level. 0 or rather, By way of example, let us consider ø S ø the fan DRV 400/30-4 listed on page LWA LA + 10 lg = LA + LS in dB S0 49 of TLT Turbo GmbH’s catalogue of In other words, sound power level LW centrifugal roof units. Its overall so- can be approximated as the sum of und power level LWtot is specified as measuring surface sound pressure 95 dB (above roof level). level øL and measuring surface level We can thus derive the following rela- LS. tive sound power levels LWrel at the From this relationship it can be con- frequencies stated: cluded that for a given sound power 63 Hz:95 dB Ð 11,9 dB = 83,1 dB level, assuming spherical or hemis- 125 Hz:95 dB Ð 4,9 dB = 90,1 dB pherical sound propagation into free 250 Hz:95 dB Ð 7,3 dB = 87,7 dB space (ideal sound propagation), the 500 Hz:95 dB Ð 8,2 dB = 86,8 dB sound pressure level decreases by 6 1000 Hz:95 dB Ð 9,2 dB = 85,8 dB dB when the distance from the source 2000 Hz:95 dB Ð 13,9 dB = 81,1 dB is doubled. 4000 Hz:95 dB Ð 12,6 dB = 82,4 dB This value may increase due to sound 8000 Hz:95 dB Ð 11,8 dB = 83,2 dB absorption by the air or floor, or diminish due to reflection from obstacles. 4. Weighted sound power level LWA Moreover, the decrease in sound By carrying out the evaluation explai- pressure level may be amplified or at- ned for the sound pressure level, tenuated by weather influences. 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 á ␯ á S

p ␯ ␦

where = q á c with ␦ = air density c = sound velocity in air becomes:

p2 W = q␦ á c á S Acoustic fundamentals 12

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 wide- ly. For calculation purposes, one starts by determining the relative sound power level of the fan, then de- ducts 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 li- ne the duct with insulating material (e.g., rock wool matting) on its air- carrying side. For straightforward sheetmetal ducts without insulating lining, the damping effect per meter of ducting can be summarized thus: Level difference [dB/m] Octave center frequency [Hz]

2.2 Duct elbow section

A duct elbow affording favourable 2 flow conditions has a slight attenuating effect on high frequencies, but low frequencies (long waves) are transmitted virtually unchanged.

d=1,0m d=0,5m d=0,25m d=0,1m

Level difference [dB/m] 0 63 125 250 500 1000 2000 4000 Octave center frequency [Hz] 13 Acoustic fundamentals

2.3 Angular deflector An angular deflector providing unfa- vourable flow conditions has a more pronounced sound-damping effect, although again, mainly high frequencies are reduced. 3 Level difference [dB/m]

Octave center frequency [Hz]

2.4 Branch fittings In a Y-fitting, sound energy is split in the ratio of the outgoing duct cross sections. Level difference [dB/m]

Ratio of cross-sections Acoustic fundamentals 14

2.5 Changes in cross-section Here again, a frequency-independent attenuation occurs. Level difference is determined by the ratio of surface areas. 3

2.6 Silencers Silencers are designed to achieve maximum sound damping. Specific configurations can be adopted to pro- vide different damping characteri- Level difference [dB|m] stics. Technical specifications are stated in the manufacturer’s catalo- Ratio of cross-sections F1 F2 gues.

By way of example, let us consider Frequency in Hz 63 125 250 500 1000 2000 4000 8000 the damping behaviour of a silencer with a mounting length of 500 mm: Attenuation in dB 6 8 11 23 32 34 26 16 2.7 Outlet reflection As the sound is emitted into the room, a portion of the sound waves is reflected back into the duct. This damping effect is referred to as ‘outlet reflection’. It affects mainly low frequencies and depends on the unobstructed outlet or inlet surface area, respectively. Level differences associa- ted with outlet reflection are summarized in the diagram across:

Duct

Room Level difference [dB/m]

Frequency á Surface [Hz á m]

These values apply to free outlet conditions only. Any built-in grids, screens Frequency in Hz 63 125 250 500 1000 2000 4000 8000 or dampers will add to the attenuating Attenuation in dB 33 19 17 14 14 12 11 10 effect. Many outlet manufacturers specify the sound-damping effect of their outlets with the outlet reflection included. Consider this example for a For space reasons, only a small sel- information the reader is referred to control valve of the type used in resi- ection of system components can be the specialized literature. dential building applications: considered here. For more detailed 15 Acoustic fundamentals

VII. Conversion of sound power into sound pressure levels (indoors) 1. General In the foregoing section we have seen how the sound power level emitted in- 3 to the room can be determined by deducting level differences due to connected system components, including outlet reflection, from the ori- ginal sound power level. However, since the human ear can only perceive sound pressures, not sound power, the resulting sound power level must be arithmetically converted into a sound pressure level. As discussed in section IV, room influences come into the game here, viz. Equivalent absorption surface area A, which determines the acoustic softn- ess or hardness of the room distance r from the air inlet or outlet, respectively, to the agreed reference point, and the orientation of the air inlet or outlet, respectively, to that reference point (expressed via the directional factor Q). 2. Directional factor The directional factor Q is an indicator

of the orientation of the duct outlet re- Directional factor lative to the reference point and vice versa. Four outlet positions have been defined: center of the room (1) center of wall (2) edge of room (3) corner of room (4) Frequency á sound outlet surface area The outlet orientation relative to the reference point P is commonly desig- nated by the emission angle α = 0¡ or 45¡. The directional factor is determined from the diagram shown across, which has as its horizontal dimension the product of frequency and square root of the outlet surface area (in m2). Acoustic fundamentals 16 [dB] p -L 3 w sabin] 2 Equivalent absorption surface A [m Sound level difference L

(free field) Directional factor Q

Distance from sound outlet surface [m]

3. Conversion dividual frequency constituents (refer to section III, part 4), and state that When the factors discussed above the cumulative level is equal to a gi- are known, the conversion of sound ven number of dB according to the A, power levels into sound pressure le- B or C weighting. vels can be carried out by the following formula: 5. Example

Q 4 Ð1 Directional factor: Q = 4 LW Ð Lp = 10 x log + (4 ␲ r2 A ) Distance from sound outlet surface: r = 2 m This fairly complex equation is solved Equivalent absorption surface: graphically in the above diagram. A = 20 m2 sabin 4. Evaluation Result: Sound level difference LW = 5 dB By deducting the level difference from the outlet sound pressure level, we obtain the relative sound pressure level. This relative sound pressure level can now be evaluated in a variety of ways. On the one hand, we can compare it to the various weighted curves (refer to section IV) and determine that the sound pressure level in the room cor- responds to a specific DIN, NC or ISO curve. On the other, we can evaluate this level against curve A, B or C, per- form the logarithmic addition of the in- 17 Acoustic fundamentals

VIII. Calculation examples Centrifugal roof-mounting fan 1. Ventilation of residential units Typ DRV 250/28-4 E The aim is to determine the noise ex- posure caused by a DRV type centrifugal roof-mounted fan in a combined Silencer kitchen and living room on the top flo- 3 or of a high-rise building. The installation situation is outlined in the sketch across. Calculation: The overall sound power level at 1350 rpm is 84 dB. Since the free-inlet volume flow of 2100 m3/h decreases to 1050 m3/h as a result of the re- sistances to be overcome, the actual sound power level at point ቢ is 84 dB Ð 7 dB = 77 dB.

The relative sound power level at point ቢ amounts to the following values, at the frequencies stated: Frequency 63 125 250 500 1000 2000 4000 8000 Hz

Lwtot 77 dB

L -2 -5,7 -11,1 -18,9 -24,3 -26,9 -26,2 -39,7 dB

Lwrel 1 75 71,3 65,9 58,1 52,7 50,1 50,8 37,3 dB

The damping effect of the silencer shown can be quantified as follows (refer to section VI, part 2.6):

Frequency 63 125 250 500 1000 2000 4000 8000 Hz

LS 6 8 11 23 32 34 26 16 dB

Lwrel 1 Ð LS = Lwrel 2 69 63,3 54,9 35,1 20,7 16,1 24,8 21,3 dB

The duct cross-section changes between silencer inlet ᕄ‚ and main shaft outlet ᕅ. The resulting attenuation depends on the ratio of the cross-sectional areas. Since the main duct measures 200 x 200 mm, its cross-sectional area is 40.000 mm2.

The cross-sectional area of the silencer is 400 x 350 = 140,000 mm2, giving a ratio of 0.286. According to section IV, part 2.5., the resulting level difference ᕅ (not frequency-related) is 2 dB. LWrel at thus assumes the following values at the frequencies stated:

Frequency 63 125 250 500 1000 2000 4000 8000 Hz

LQ 22 2 2 2 2 2 2dB

Lwrel 2 Ð LQ Lwrel 3 67 61,3 52,9 33,1 18,7 14,1 22,8 19,3 dB Acoustic fundamentals 18

Attenuation also occurs in the sheetmetal ducting of the main shaft (refer to VI, 2.1). Frequency 63 125 250 500 1000 2000 4000 8000 Hz LK’ 0,6 0,6 0,45 0,3 0,2 0,2 0,2 0,2 dB/m

LK = 3 2,5 m á LK’ 1,5 1,5 ~1,1 ~0,8 0,5 0,5 0,5 0,5 dB Lwrel 3 Ð LK = Lwrel 4 65,5 59,8 51,8 32,3 18,2 13,6 22,3 18,8 dB Sound damping takes place in the elbow between main shaft and the secondary shaft as follows (refer to VI, 2.2): Frequency 63 125 250 500 1000 2000 4000 8000 Hz LB 00001233dB Lwrel 4 Ð LB = Lwrel 5 65,5 59,8 51,8 32,3 17,2 11,6 19,3 15,8 dB Further damping occurs in the sheet metal ducting of the secondary shaft (refer to VI, 2.1): Frequency 63 125 250 500 1000 2000 4000 8000 Hz LK’ 0,6 0,6 0,45 0,3 0,3 0,3 0,3 0,3 dB/m LK = 2,5 m á LK’ 1,5 1,5 ~1,1 ~0,8 ~0,8 ~0,8 ~0,8 ~0,8 dB Lwrel 5 Ð LK = Lwrel 6 64,0 58,3 50,7 31,5 16,4 10,8 18,5 15 dB At the damper valve ᕉ, sound waves are attenuated by the damper valve itself and by outlet reflection (refer to VI, 2.7): Frequency 63 125 250 500 1000 2000 4000 8000 Hz LV 33 19 17 14 14 12 11 10 dB Lwrel 6 Ð LV = Lwrel 7 31,0 39,3 33,7 17,5 2,4 0 7,5 5 dB ᕉ LWrel 7 at is the relative sound power level emitted into the room. This shall now be converted into the relevant sound pressure level at the reference point. For this first the directional factor Q has to be determined. The emission angle α = 0¡since the control damper valve is located in the middle of the wall (bottom diagram in VII, 2, curve 2). Sound outlet surface area is 0.01 m2, square root of 0,01 m2 = 0.01 m2 = 0.1 m. According to the diagram, this gives the following values at the frequencies stated: Freq. = 63 125 250 500 1000 2000 4000 8000 Hz f x √F’ = 6,3 12,5 25 50 100 200 400 800 Hz x m Logarithmic addition of the levels (re- Q 1,8 2 2,4 3,2 4,8 6 7 7,8 fer to III, 5) yields the following From the diagram in VII, 3 the level difference can be determined, using the equivalent absorption surface A = 10 m2 sabin and the distance r = 1 m. Re-

sults for the individual frequencies are as follows: 1,9 20,2 22,6 12,3 0,9 0 7,5 2,9 Frequency 63 125 250 500 1000 2000 4000 8000 Hz

LW Ð Lp = 3 3 2,5 2,0 1,5 1,5 1 1 dB 20,2 23 0,9 8,8

Lprel 28,0 36,3 31,2 15,5 0,9 0 6,5 4 dB We have thus determined the sound pressure level, which can be evaluated in a number of ways. Let us first compare it with the weighted curves from IV, 3. 24,8 9,4 ISO curve: The actual sound pressure level remains below ISO N-25. NC curve: 24,9 The actual sound pressure level remains below NC 20 at all frequencies. dB 19 Acoustic fundamentals

DIN curve: The actual sound pressure level remains below DIN 35 at all frequencies. Apart from this comparison with acceptable frequency responses, it is possible to add the levels, e.g. according to curve A: Frequency 63 125 250 500 1000 2000 4000 8000 Hz A Ð weighted.:-26,1 -16,1 -8,6 -3,2 0 +1,2 +1 -1,1 dB 3

Lprel A: 1,9 20,2 22,6 12,3 0,9 0 7,5 2,9 dB

2. Axial flow fan The exhaust air from a factory hall is extracted by an axial flow fan via connected exhaust ducts. Schematic view (side view) of the building. 40 Screen 0,2 x 0,9 m

8 m C

A Axial-flow impeller

B Flexible duct connector

C Exhaust air duct 60 m

D Flexible duct connector Building depth 24 m, absorption surface A = 200 m2 sabin

Axial fan Ð detailed view 1000 ¯

B A D

Selected axial flow fan Rotational speed: 950 rpm Total pressure increase: 500 Pa (TLT Turbo GmbH catalogue ãAxial Blade angle: 20 ¡ Overall sound power level: 99 dB Flow Fans“) Volume flow: 40 000 m3/h To be determined: sound pressure AXN 12/56/1000 MD Motor rating: 7,5 KW level in the room and at outlet point

2.1 Sound pressure level inside Relative sound power level emitted into the silencer: the factory hall Frequency 63 125 250 500 1000 2000 4000 8000 Hz

LWtot 99 dB Lwrel -8,7 -6,4 -5,1 -8,2 -12,7 -15 -16,8 -19,8 dB ᕃ Lwrel A 90,3 92,6 93,9 90,8 86,3 84 82,2 79,2 dB Acoustic fundamentals 20

Attenuation in the silencer and influence of airflow noise:1) L silencer -4 -6 -11 -20 -30 -24 -15 -10 dB ᕄ Lwrel B 86,3 86,6 82,9 70,8 56,3 60 67,2 69,2 dB Airflow 3 noise 67 58 55 60 64 56 49 40 dB Sum of levels 86,3 86,6 82,9 71,1 64,6 61,5 67,2 69,2 dB The sound attenuation caused by the sheetmetal ducting is neglected here.

Attenuation due to flow splitting and outlet: (refer to page 15/16) LW split -16 -16 -16 -16 -16 -16 -16 -16 dB LW outl. -13 -8 -4 -1 0 0 0 0 dB ᕅ LWrel C 57,3 62,2 62,9 54,1 48,6 45,5 51,2 53,2 dB These findings are now to be converted into the sound pressure level prevai- ling in the middle of the room, height: 2 m, 45¼, S = 200 m2. For simplification, the 40 outlets are combined into four groups of 10 each. Distances are 10 and 23 m, A-weighing is used. Directional factor ␣ 2 2,2 2,6 3 3,6 4 4 4 Addition of 10 +10 +10 +10 +10 +10 +10 +10 +10 dB A- weighting -26,1 -16 -8,6 -3,2 0 +1,2 +1,0 -1,1 dB

LW Ð Lp 10 m -17 -17 -17 -17 -16 -16 -16 -16 dB

LW Ð Lp 23 m -17 -17 -17 -17 -17 -17 -17 -17 dB

Lprel A 10 m 24,4 39,5 47,3 43,9 42,6 40,7 46,2 46,1 dB

Lprel A 23 m 24,2 39,5 47,3 43,9 41,6 39,7 45,2 45,1 dB Addition of the 4 sources: 30,2 45,5 53,3 49,9 48,1 46,2 51,7 51,6 dB

Calculation of the cumulative level LpA 58,1 dB ~ 58 dB 1) from TLT catalogue

2.2 Outdoor sound pressure level Distance 4 m, 0¡

Sound power level at point ᕆD as previously calculated for point ᕅC : ᕆ Lwrel D 86,3 86,6 82,9 71,1 64,6 61,5 67,2 69,2 dB Outlet attenuation, A-weighting and conversion into sound pressure level: L outl. -7 -3 -1 0 0 0 0 0 dB LA -26,1 -16,1 -8,6 -3,2 0 +1,2 +1 -1,1 dB

LW Ð Lp -20 -17 -16 -16 -15 -15 -15 -15 dB

Lprel A 33,2 50,5 57,3 51,9 49,6 47,7 53,3 53,1 dB

Calculation of the cumulative level LpA: 61.3 dB ~ 61 dB. 21 Acoustic fundamentals

IX. Fans as sound sources - summary and addenda 1. General A fan generates noise as a result of aerodynamic influences (turbulent and vortex noise, blade-passing noi- 3 se) and mechanical factors (blade, bearing and motor vibrations). Such noise can propagate in the following manners: a) as airborne noise emitted directly from the fan inlet opening into the installation room b) as airborne noise transmitted to the inlet/outlet points via connected ducting c) as structure-borne/airborne noise transmitted into the surrounding rooms via the fan casing wall or connected ducting, respectively d) as structure-borne noise transmitted into the surrounding room structure via ducting and founda- tion anchoring

2. Airborne noise b) the A-weighted (cumulative) sound tave-band analysis being provided for pressure level L in dB L (see example). Noise emissions of fans, including air- PA Wrel z á n -1 borne noise, are assessed and calcu- c) the relative sound pressure level fD = 60 in s or Hz, respectively lated in terms of sound power levels. LpArel in dB. Fan manufacturers state this data in where z = number of impeller blades the following forms: taking account room influences (ab- n = rotational speed of the fan sorption, direction, distance) in rpm. a) overall sound power level LW in dB (decibels) Airborne sound waves propagate equally from the fan in the inlet and b) A-weighted overall sound power outlet directions via the connected

level LWA in dB ducting. If the fan draws air freely from the room, the noise situation in c) relative sound power level L in Wrel the room itself may become critical. dB. Baseline parameter for the calculati- Upon completion of the acoustical on of sound-attenuating measures is calculations these values must usual- the overall sound power level LW of ly be converted into sound pressure the fan, which is usually stated for the levels, viz. operating point in the diagram of characteristic curves. a) the relative sound pressure level Variables L and L are usually ex- LPrel in dB compared with the per- WA Wrel mitted limit curves (NC, ISO-N, pressed as a function of the ãmain in- etc.) terference frequency“ fD (frequency of rotation) and the fan size, with an oc- Acoustic fundamentals 22

Example (from Centrifugal Fans Portion Fan* PortionAnteil 2.2 2.2 at bei an Oktavmittelfrequenz octave center frequency Hz of [Hz]* catalogue), manufacturer: TLT- Bau- z á n Anteil* size fD = Hz größen 60 2.1 Turbo GmbH 63 125 250 500 1000 2000 4000 8000 500 5,1 19,6 16,1 13,2 5,5 10,3 14,2 18,2 22,2 Sound power level emitted from 250 8,2 19,7 16,1 7,3 10,6 13,3 17,3 21,3 25,3 the fan opening 315 125 11,5 19,8 10,2 12,4 13,7 16,4 20,4 24,4 28,4 63 14,6 13,9 15,3 15,4 16,8 19,5 23,5 27,5 31,5 3 To determine the noise level at the in- 500 4,7 18,0 14,6 12,1 4,9 10,2 14,2 18,2 22,2 250 7,8 18,1 14,7 6,2 10,0 13,3 17,3 21,3 25,3 stallation site of a centrifugal fan, it 400 125 11,1 18,2 8,8 11,3 13,1 16,4 20,4 24,4 28,4 will usually be necessary to know the 63 14,2 12,4 13,8 14,4 16,2 19,5 23,5 27,5 31,5 sound power level at its inlet or outlet 500 4,5 16,6 13,3 11,3 4,5 10,2 14,2 18,2 22,2 250 7,5 16,7 13,4 5,4 9,6 13,3 17,3 21,3 25,3 opening. The data given in the follo- 500 125 10,8 16,8 7,5 10,5 12,7 16,4 20,4 24,4 28,4 wing tables assume Case 1 outlet ab- 63 13,9 10,9 12,6 13,5 15,8 19,5 23,5 27,5 31,5 500 4,4 15,0 12,2 10,5 4,2 10,2 14,2 18,2 22,2 sorption conditions according to VDI 250 7,2 15,1 12,3 4,6 9,4 13,3 17,3 21,3 25,3 2081 (refer also to page 14). 630 125 10,5 15,2 6,4 9,7 12,4 16,4 20,4 24,4 28,4 63 13,7 9,4 11,4 12,8 15,5 19,5 23,5 27,5 31,5 Levels are determined as follows: 500 4,3 13,6 11,1 9,9 4,2 10,2 14,2 18,2 22,2 800 250 7,1 13,7 11,2 4,0 9,3 13,3 17,3 21,3 25,3 125 10,3 13,8 5,8 9,1 12,4 16,4 20,4 24,4 28,4 LW Vent dB = fan’s overall sound 63 13,5 7,9 10,4 12,2 15,5 19,5 23,5 27,5 31,5 power level, taken 500 4,3 12,3 10,3 9,5 4,2 10,2 14,2 18,2 22,2 from characteristic 250 6,9 12,4 10,4 3,6 9,3 13,3 17,3 21,3 25,3 1000 125 10,2 12,5 4,5 8,7 12,4 16,4 20,4 24,4 28,4 curve diagrams 63 13,4 6,7 9,5 11,8 15,5 19,5 23,5 27,5 31,5 500 4,3 11,2 9,5 9,2 4,2 10,2 14,2 18,2 22,2 LWA open dB = fan’s A-weighted 250 6,9 11,39,6 3,3 9,3 13,3 17,3 21,3 25,3 1250 125 10,1 11,43,7 8,5 12,4 16,4 20,4 24,4 28,4 sound power level 63 13,2 5,6 8,8 11,5 15,5 19,5 23,5 27,5 31,5 fan, emitted from its 500 4,3 10,1 8,9 9,2 4,2 10,2 14,2 18,2 22,2 opening into the 250 6,8 10,2 9,0 3,3 9,3 13,3 17,3 21,3 25,3 1600 125 10,0 10,3 3,1 8,4 12,4 16,4 20,4 24,4 28,4 room according to 63 13,2 4,5 8,2 11,5 15,5 19,5 23,5 27,5 31,5 the equation * Values for intermediate fan sizes must be obtained by interpolation. LWA open = LW Vent Ð portion 2.1 dB wherein the value of portion 2.1 is taken from the table across. LWrel open dB = relative sound power level of the fan, emitted from its opening into the room according to the equation Calculation example L = L Ð portion 2.2 dB W rel open W Vent Centrifugal fan, size 800 wherein the value of V = 10 m3/s, pt = 1750 Pa, portion 2.2 is taken n = 1400 rpm, z = 8 from the table

across. From the diagram of characteristic curves: LW = 108 dB In the case of double inlet fans, the f = z á n = 8 á 1400 = 187 Hz D 60 60 overall sound power level thus determined must be increased by 3 dB. LWA open = LW Ð portion 2.1 = 108 Ð 9,5 = 98,5 dB

Lwrel open = LW Ð portion 2.2: Frequency: 63 125 250 500 1000 2000 4000 8000 Hz

LW: 108 dB Lwrel: 13,7 8,5 6,5 10,8 14,8 18,8 22,8 26,8 dB (portion 2.2)

Lwrel: 94,3 95,5 101,5 97,2 93,2 89,2 85,2 81,2 dB 23 Acoustic fundamentals

The standard method of reducing sound emissions from the fan opening is to mount an inlet silencer. In ventilation and air conditioning, the propagation of airborne noise to inlet and outlet points via connected ducting is usually the critical parameter. 3 The outlet noise situation can be calculated by analogy with the above example.

In-duct sound power levels PortionAnteil PortionAnteil 1.2 1.2 at bei an Oktavmittelfrequenzoctave center frequency Hz of [Hz] f = z á n Hz Sound power level emitted into the D 60 1.1 ducting by a centrifugal fan is a key 63 125 250 500 1000 2000 4000 8000 starting parameter for calculating le- 500 4,3 7,2 8,2 9,2 4,2 10,2 14,2 18,2 22,2 vels in connected ductwork or silen- 250 6,8 7,3 8,3 3,3 9,3 13,3 17,3 21,3 25,3 125 9,9 7,4 2,4 8,4 12,4 16,4 20,4 24,4 28,4 cers. 63 13,0 1,6 7,5 11,5 15,5 19,5 23,5 27,5 31,5 Levels are determined as follows: LW Vent dB = overall sound power level of the fan, taken from characteristic curve diagrams LWA Vent dB = A-weighted sound power level determined according to the equation LWA Vent = LW Vent Ð portion 1.1 dB wherein the value of portion 1.1 is taken from the table across. Calculation example L dB = W rel Vent Centrifugal fan, size 800 relative sound power level determined according to the equation V = 10 m3/s, pt = 1750 Pa, n = 1400 rpm, z = 8 LW rel Vent = LW Vent Ð portion 1.2 dB L = 108 dB wherein the value of portion 1.2 is ta- W ken from the table across. LWA open = LW Ð portion 1.1 = 108 Ð 8,3 = 99,7 dB

LWrel = LW Ð portion 1.2

Frequency: 63 125 250 500 1000 2000 4000 8000 Hz

LW : 108 dB LWrel: 7,3 5,4 5,8 10,8 14,8 18,8 22,8 26,8 dB (Portion 1.2)

LWrel : 100,7 102,6 102,2 97,2 93,2 89,2 85,2 81,2 dB Acoustic fundamentals 24

The standard method of reducing sound emissions from the fan into connected ducting is to mount an in- duct silencer.

3. Sound emission In many cases, the noise emitted by the fan casing wall or connected ducting is the critical factor. The basic parameter for calculating effective attenuation countermeasures is the sound power behind the emitting wall. The wall itself has a damping effect which essentially depends on its thickness. Apart from the sound power level, the amount of sound energy emitted into a room in this manner is a function of the wall surface area. The standard method of reducing sound emissions from fan casing or duct walls consists in insulation or in the installation of a „high-gravity“ material. Whereas sound emission from the fan opening and acoustic output into the ducting can be taken from the re- spective catalogues, sound emission from the fan casing must be obtained from the manufacturer (TLT Turbo GmbH, Bad Hersfeld). Special software is available for determining this parameter in each individual case. 25 Acoustic fundamentals

4. Structure-borne noise transmission/vibration insulation Sound waves transmitted through ri- gid connecting elements are referred to as structure-borne noise. In fact, this phenomenon involves the propagation of vibrations. In the case of 3 fans, this occurs via two transmission routes. Firstly, vibrations spread from the fan to the ducting via the fan inlet and outlet connections. Elastic duct connectors can prevent this effect. It should be noted, however, that basic elastic duct connectors will permit an almost unobstructed passage of noise into the room. This can be reme- died by using appropriate insulation, or by arranging the elastic connector downstream of a silencer. Secondly, fan vibrations are transmitted to the foundations from where they are conducted to other parts of the building brations. In other words, they minimi- tion mounts are usually employed. At structure. Here the preferred remedy ze the transmission of fan vibrations speeds above 1000 rpm, rubber is to erect the fan on anti-vibration caused by residual imbalances and mounts are preferred. Cork slabs are mounts. The latter serve two purpo- bearing vibration while counteracting used for fans exceeding 3000 rpm ses, viz. to prevent the transmission structure-borne noise at the same ti- and very heavy units. of structure-borne noise and to provi- me. For fans operating at speeds be- de insulation against mechanical vi- low 1000 rpm, spring-type anti-vibra-

In dimensioning and installing anti-vi- ␭ recommended The expression no = ne / bration mounts, care must be taken to range ensure an even load distribution, level with ground, and a high insulating efficiency. no = natural frequency of anti-vibra- Insulating efficiency is a measure in- tion mount (in Hz) dicating the percentage of interferen- ne = fan speed in rpm ce forces actually absorbed by the n mounts. The ratio between fan rpm ␭ e insulating efficiency in % = no and the natural frequency of the anti- vibration mounts should be greater can be used to calculate the neces- than 2.5; this will give an insulating ef- sary natural frequency of anti-vibra- ficiency in excess of 80%. tion mount. Suitable mounts can then be selected from the manufacturers’ catalogues using this frequency and the load per mount (overall weight of the fan unit, including frame and motor, divided by the number of anti-vibration mounts). Acoustic fundamentals 26

X. Technical information in Where sound pressure levels are in- All values are stored in TLT’s „Aku- TLT product catalogues dicated, these are defined in detail stik“ software program. due to their dependence on distance, Starting point for all calculations is the direction and room characteristics. The accuracy of TLT’s acoustic data is vouchsafed by tests and measure- overall sound power level LW in decibels (dB), which is stated in the cha- Sound data given in TLT fan catalo- ments spanning more than 30 years 3 racteristic curves for all fans in TLT gues reflect the results of hundreds of of fan development. catalogues. measurement series. A large number of values is derived from in-duct tests, Furthermore, the catalogues indicate supported and supplemented by in- the A-weighted and relative sound numerable measurements by the en-

power levels LWA and LWrel, respec- veloping surface or free-field method. tively, emitted from the fan opening or Case studies on actually implemen- into the ducting as the case may be. ted systems were likewise taken into account.

Low-reflection air duct connection per Insulation Specimen DIN 45635, Part 9 roof-mounting Measuring Antidrum Airtight Nozzles centrifugal fan duct compound door Friedrichs probe

Sound measuring duct Damping chamber, calibrated

DRV type centrifugal roof-moun- volume and pressure measurements pressure (ps) and dynamic pressure ting fan with inlet-side measuring and DIN 45 635, Part 9 (draft) for (pd) in the inlet duct. airway sound measurements. Our test rig for roof-mounting centrifu- Pressure increase (pt 1) is calculated gal fans conforms to DIN 24 163 for from the difference between static

Chamber test-rig with specimen View of the chamber-type test rig