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 „to- 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 pres- sure 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 „po- 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 „threshold 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 expres- sed in relation to the threshold pres- sure of audibility. Thus, it is said that a given sound has a pressure of, e.g., 10, 1.000 or 100.000 times the thres- hold pressure of audibility. To obtain smaller numbers, the ratio thus obtai- ned is logarithmized. The value of the resulting logarithm is referred to as a the sound power level. We can thus write the following equa- tion: 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 constitu- ents. In practice this is done with the aid of microphones combined with suitable upstream filters so as to re- 3 cord only sound constituents („to- nes“) of a given frequency. These constituents are then measured. 7. 2.816 – 5.600 Hz 4. Phon Octave center frequency = 4000 Hz The phon is a unit related to dB. It cor- 8. 5.600 – 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.