The NAG-DAGA congress, March 2009 in Rotterdam and these web pages

This page is made to make sounds audible. It is coupled to a paper (with the same title) that was written for the NAG-DAGA congress that was held in Rotterdam from 23-28 March 2009. The main part of the text is copied here. However it is somewhat extended to incorporate more sound samples than dealt with in the original paper. The paper was written by Lau Nijs of Delft University of Technology, Netherlands and Monika Rychtáriková of the Katholieke Universiteit Leuven, Belgium.


The present website is just one "stand-alone" page. However, it is also embedded in a more extended website, written for students in Architecture. Unfortunately for foreign visitors, this website is in Dutch, but yet:

Wees welkom op de site:


Introduction to sound in a sports hall

In the Netherlands and Belgium the standards for sports facilities are given as maximum values for the reverberation time. Since the dimensions of sports facilities may vary considerably (from 1000 to 100,000 m3) and the reverberation time depends on the volume, they are given as increasing values with increasing dimensions. Actually the underlying idea is that the mean absorption coefficient should be about 25% for all dimensions [1], [2], [3].

In the design stage of a hall, calculations are made by summing the absorptive surfaces. In many cases Sabine's equation is used to calculate the reverberation time, but sports halls have usually non-cubic dimensions and absorbing materials are always inhomogeneously distributed, since the floor is non-absorbing and the ceiling is preferred for absorption. Hence the reverberation time may increase considerably compared to Sabine's. The international standard ISO 12354-6 [4] provides a method to calculate this effect.

If the reverberation time appears too long, it seems as if the effect of the absorption is lower than calculated in the design stage. However, adding absorption is not necessarily a solution; the distribution through the hall may be more important. In this paper three aspects will be discussed: the reverberation time, the sound pressure level and the occurrence of (flutter) echoes. Some architectural solutions will be given to overcome long reverberation times. It appears very instructive to listen to sound samples from auralizations in a virtual hall, so during the actual congress presentation some samples are presented. In the present website similar sounds are given.


Sound pressure level, reverberation time and (flutter) echoes

In a sports hall the sound pressure level plays an important role. The sound may come from a "wanted source" (speech for instance) or from other "noise sources" in the hall:



The value LW represents the acoustic sound power level of the source. The source-receiver distance is given by r, while Q stands for the directivity of the source. For a human talker a value Q = 2.5 is often taken in front of the mouth (for A-weighted levels). A is the total absorbing surface and α represents the mean absorption coefficient when A is divided by the total geometrical surface. There are numerous books that give more details. Our own work is described in more detail in [5].

Eq. (1) predicts a constant value of SPL for big values of r. This contradicts experience, so Barron [6] developed an alternative, which in our case [7] is written as: 



with mfp = 4V/S, the mean free path. Equations (2) and (3) are equal if r = mfp.

In the design stage, A is calculated from the absorption coefficients of all materials. If the hall is finished, measuring the contributions of all surfaces separately is almost impossible and the total value A is measured instead from the reverberation time. In many cases Sabine's formula is used:



with mfp = 4V/S, the mean free path. Equations (2) and (3) are equal if r = mfp.

with V the room's volume.

Another characteristic determining the acoustical quality is the occurrence of "flutter echoes". In very reverberant halls they cannot be heard, but if all absorption is put on the ceiling echoes may be found along the length and width dimensions of the hall. They can be heard in practice and can be seen in plots of decay curves, but at present there is no method to quantify them. The phrase "flutter echoes should not be heard", as used in older standards is too informal for (legal) standards.


Sound decay in a sports hall, an example

A number of situations have been calculated in a ray-tracing model (Catt acoustic) of a big sports hall of 70 × 25 × 12 m3. The floor plan is given in figure 1. The program produces many acoustical variables, but our focus is on the reverberation time (-5 to -35 dB) and the sound pressure level. Energy impulse responses from the program are used to study the echoes in the hall. Auralizations are made by convolution of the impulse responses from the program and "dry" sound samples.

A wanted source is at position A. It is represented by speech originally recorded in the anechoic rooms in Delft and Leuven. Noise signals are generated at position B. These signals are represented by four talkers or by impulsive sounds from a basketball dribble. Microphone positions are as indicated; one position (number 14) is at the mean free path distance mfp from the source, which is 14.5 in this hall. The source height is 1.5 m; microphone height is 1.2 m. In sports halls the reverberation time often depends on source and microphone height, since there is no influence of  diffusing elements in the hall. These effects have been measured in real halls, but are also found in computer models.


Figure 1: A sports facility used for ray-tracing simulations plus auralizations. The main source is at position A. If noise is added it is generated at position B. For microphone position 14, the source-receiver distance equals 14.1 m, which is almost equal to the mfp-value. All scattering coefficients are 10%.


The first computer runs were made to show the effect, in figure 2, of the amount of absorption plus the distribution along the surfaces.

  • Situation (a) is when floor, ceiling and walls all have a 7% absorption coefficient.

  • The same is done for situation (b) but now all absorption coefficients equal 28%.

  • In situation (c) the mean absorption coefficient is again 28% but the floor and four walls have 10% absorption and all the other absorption is on the ceiling with 70% absorption.

  • Situation (d) is more a hypothetical case. It has the lowest absorption (18%) on ceiling and floor, a medium value (34%) on the side walls and the highest value (68%) on the two smallest surfaces. Now, the mean absorption is 28% again, but the decay times are equal in all three directions. This leads to the minimum reverberation that is possible. Some more mathematical information can be found in a congress paper on this subject [8].


The left hand figure 2 gives the response to an energy pulse as calculated in the ray tracing model for microphone 14. The right hand figure 2 shows the schroeder curves as derived from the left hand curve by backward integration. These are the curves that should be used to derive the reverberation times by curve fitting along the four slopes. The differences are immense; RT-values are 6.90, 4.55, 2.71 and 1.66 s. A complicating factor is that curves (a) and (d) are straight lines, but curves (b) and (c) are concave.

The SPL-levels can be derived from the schroeder values at t = 0. In case (a) this level is 47.8 dB; for case (b) we find 42.4 dB, cases (c) and (d) differ only by a few tenths of a decibel from case (b). This is a remarkable result. If A is calculated from the RT-values (reversing Eq. 3) and input in Eq. (2), the SPL-values would differ considerably. The reason is that RT is found from the curves after 0.3 s, while the SPL values are mainly determined by the early reflections before 0.3 s. As can be seen in the left hand figure there are only minor differences for cases (b), (c) and (d) before 0.6 s.


Figure 3 gives the same results of SPL and RT for the four situations (a) to (d), but now combined in one SPL-RT-graph, which is very instructive to compare measured and calculated microphone positions in a room. The four microphone positions 1, 2, 3 and 18 (from figure 1) are added to microphone position 14.

Figure 3 also shows two theoretical curves where equations (2) and (3) are calculated for mean absorption coefficients of 7 % and 28 %. The value of RT is found as one value for all receiver positions (RT is 6.9 and 2.0 s respectively), since there is no influence of the distance in equation (3).


Figure 2: Echograms ( left) and schroeder curves (right) as calculated from the four cases as given in the text. Microphone position is number 14. Reference sound level is taken as 60 dB at 1 m in an anechoic chamber.


Figure 3: SPL and RT for the four cases explained in the text, for the five microphone numbers indicated in figure 1. Position 14 is given as full dot, the other four as open circles. Both horizontal lines are calculated with equations (2) and (3) using 7% and 28% mean absorption.


The results from figure 3 can be summarized as:

  • The reference level is 60 dB at 1 m in the anechoic chamber. Levels at microphone position 1 are slightly higher due to the hall's reflections.

  • Eq. (3) predicts a constant reverberation time through the entire hall. This is not the case in the ray-tracing results.

  • Curve (a) and the 7% curve agree quite well. This is where Sabine's theory is most reliable, since reverberant situations lead to diffuse fields.

  • All four curves (a) to (d) show a slight increase of SPL at the mfp distance. This is due to the non-cubic space as explained in [9].

  • The reverberation times of curves (b), (c) and (d) appear to depend strongly on the distribution of absorbing materials. In the special case (d) the reverberation time is even below the one predicted by equation (3). Actually ray-tracing theory predict a minimum value equal to Eyring's reverberation time instead of Sabine's. Eyring's value is always lower.

  • RT values at position 14 are: 7.3, 4.5, 2.7 and 1.7 s for situations a, c, b and d. The results from the standard 12354-6. are 7.60, 3.30, 2.90 and 2.12 s. The trend is the same but the mutual differences from the standard are less. It is difficult to say which value should be preferred; we are planning scale model measurements to investigate the effect. However, situation (d) should tend to Eyring's value, but the minimum value from standard 12354-6 is Sabine's. That is not very likely. Results from another ray-tracing program (Odeon) confirm the Catt-results.

  • The striking result is that the values of SPL are almost equal for situations (b), (c) and (d) at microphone position 14 where r = mfp. Differences are greater at position 18. So SPL depends only marginally on the positioning of absorbing materials.

  • In fact this last result means that the reverberation time is not a good predictor if we want to characterize the sound pressure level in a sports facility. Measuring SPL directly gives better information. This is not very difficult in practice under one condition: the noise source must be calibrated. Simple methods with exploding balloons etc. are useful to find RT but useless for SPL.


Auralization examples to investigate acoustical echoes in sports facilities

The echograms of the left hand part of figure 2, show strong differences in echo behavior. Sound samples have been made, with the aid of the auralization techniques of the ray-tracing program, to investigate the effect in more detail. Three cases are used; the homogeneous case with 28% absorption (b) has been left out.


Auralization examples:  Calibrating the loudness of the headphone signal

The sound samples can be best listened with ear phones, but the demonstrations can only be put into perspective when the loudness is calibrated properly. In our laboratory we did that for one type Beyer headphone. The loudness is different for other types and brands. One method working reasonably for a website works as follows:

  • Put on your headphone

  • Assume a colleague at 1m distance in an office that is not reverberant.

  • Click a few times on the next calibration signal and use your computer's volume control until it sounds "reasonable"

  • Do NOT use the volume control anymore. All other levels are adjusted to the calibration signal. If a sound seems a little soft, it is done purposely and part of the demonstration.



The sound samples on this page are SOFTER than those given on pages

"02080_geluiddemonstraties.aspx" and "02210_Signaal_Ruis.aspx"

That is because in the present page speech is compared with sound from a bouncing basketball, which is much louder. Hence the sound levels of all sound samples have been decreased to avoid clipping.




Auralization examples:  Sound levels at a few distances from a human talker

Sound samples auralized at 1 m from a talker for three configurations as given in the leftmost column of the table.

The chosen configuration of the absorption in the third case leads to a minimum value of the reverberation time. It is, however, not a very realistic situation that will be found in practice.

Microphone at 1 m from source






In the following examples the sound (at the same position) is just one impulse from a basketball bounce.

The signal may be rather loud but it has been carefully calibrated against the speech of the previous signals.





Compared to the previous example the microphone position has shifted from 1 to 10  and 51 m distance.











Auralization examples:  A speech signal disturbed by noise

The speech of a "wanted" talker at 10 m is disturbed by the noise of four other speakers at 31 m. 










Annoyance from echoes depends on the character of the noise

The following examples are just like the previous examples 1 to 4, but now we will focus on the occurrence of echoes and on the question whether or not they must be considered as annoying.


Auralization examples:  Sound samples to illustrate echoes

Impulsive sounds from a basketball at 31 m are a tool to demonstrate echoes 







So from the previous examples 5_a, 5_b and 5_c it could be concluded that the special (hypothetical) case 5_c, with the main absorption perpendicular to the long axis, should be preferred. However, the character of the noise source plays an important role as will be illustrated in the following samples.





Echoes, can they be avoided?

Case (c)  from the preceding examples represents a sports hall that may be found on many occasions in practice. It is easy from an architectural viewpoint to install all absorption on the ceiling and have all the side walls constructed with hard materials. It leads to adequate noise levels in the hall, but at the cost of quite strong echoes. Case (d) represents a hypothetical case (an absorbing floor surface for instance), never found in practice, to show that echoes can be avoided in theory.

Now we will try to find some practical solutions to hunt echoes.


Several computer runs have been made from which three situations are presented here. Like the previous situations, the cases (e), (f) and (g) have a nearly reflecting floor surface and absorption on the ceiling. But now the long walls are absorbing as well (70%) to emphasize the sound transmission along the longest dimension reflecting against the two smallest walls. In case (e) these walls have a 7% absorption coefficient, which is increased to 70 % in case (f). In case (g) the small walls are non-absorbing but inclined, so the sound reflections are steered upwards to the absorbing ceiling. The length of the hall is 70 m along the floor and 78 m along the ceiling. The mean absorption has increased to 46% or even 52%. These values are very high and will seldom be found in practical cases.

Figure 5 shows the echograms from the three cases.



Figure 4:  To investigate echoes special cases have been calculated to investigate echoes along the long horizontal axis.

The upper case is NOT the same situation as case (c), where the long walls had only 10% absorption. Now the long walls have 70% and the mean absorption has increased to 46% or even 52%.



Figure 5: Echograms ( left) and schroeder curves for cases (e), (f) and (g) explained in the text. Curves are calculated at microphone position 14.


Situation (e) shows a strong (flutter) echo. When listening to the auralized sound a single echo is perceived after 400 ms plus a "metallic" sounding reverberation. There is some difference in sound between cases (f) and (g), but they have no practical meaning for the architectural design process. Both cases (f) and (g) have an audible echo at 400 ms. The only way (we could find) to avoid the echo at 400 m is to use totally absorbing walls, which is not very realistic. All other cases (including a case with total diffusion using Lambert's law) show the echo.


Auralization examples:  Echoes, can they be avoided

See figure 4 for source and receiver positions. In all cases the basketball dribble is used as input sound.





The right part of figure 5, shows that there is a big difference in reverberation times between case (e) at one side and cases (f) and (g) at the other. Case (e) has 3.8 s; the reverberation time of case (f) equals 1.1 s. It is interesting to see that case (g) has much less absorption on the two walls than case (f) and yet the reverberation time is even lower: RT = 1.0 s. These values look short in comparison with situations (a) ... (d), but that is due to the absorption on the long walls in the present case. Sabine's reverberation time in case (f) is 1.1 s. This means that the use of diffusion appears to be just as effective as absorption. There is even one Dutch sports facility where inclined advertising signs are used to avoid flutters.


In the previous section of this paper the reverberation time was called unfit to predict the amount of absorption and consequently the sound pressure levels in the hall. When it comes to flutter echoes, however, there is more correlation between the reverberation time and the existence of flutter echoes. In figure 3 the schroeder curves also give information about the total energy in the (flutter) echoes, so the existence of flutter echoes leads to a higher reverberation time.




  • The Dutch and Belgian standards give maximum values for the reverberation times in sports facilities. If that maximum value is exceeded it may be caused by a lack of absorbing surface and/or by the existence of (flutter) echoes.

  • To investigate if the lack of absorption is the main drawback of a hall, measuring the SPL gives adequate information. Measuring RT may underestimate the absorption and hence overestimate the noise in a sports hall. Measuring SPL (or rather the loudness G) is not difficult but it requires a calibrated sound source. The combination of SPL and RT in one graph gives optimal information.

  • If the amount of absorbing materials is sufficient to reduce noise levels, the reverberation time may still exceed the standard values if (flutter) echoes are present. However, there is no value to express the annoyance of flutter echoes in sports facilities in a numerical value.

  • It is hard (if not impossible) to combat early echoes that reflect only once. Multiple echoes can be avoided by extra absorption, but diffusion and well chosen inclined surfaces are equally effective.

  • Sabine's equation always underestimates the reverberation time in sports facilities, since they are always non-cubic with inhomogeneous absorption. Ray tracing methods and the standard EN-12354-6 both predict an increase of RT, but they do not agree completely. Ray-tracing models are able to predict the influence of inclined surfaces; EN 12354-6 fails in this respect.

  • Auralizations are useful to demonstrate excessive noise and flutter echoes. Since it is not clear, if flutter echoes or high noise levels are most annoying, they will be used in future investigations.



[1]      ISA-Sport, "Handboek Sportaccommodaties", Instituut voor Sportaccommodaties van NOC*NSF, Arnhem, Netherlands, 2005, in Dutch.

[2]      Nijs, L. & A. Schuur, "Het gebruik van de nagalmtijd bij de normstelling van sportzalen", Bouwfysica 15 (2004), 9-18, in Dutch.

[3]      Vermeir, G. & J. van den Bergh, J., "Classroom acoustics in Belgian schools: requirements, analysis, design", 2nd International Building Physics Conference, Leuven (2003), 869-875.

[4]      CEN, European Committee for Standardization, Building Acoustics - "Estimation of acoustic performance of buildings from the performance of elements - Part 6: Sound absorption in enclosed spaces, EN 12354-6", 2004.

[5]      Nijs, L, K. Saher, D. den Ouden, "Effect of room absorption on human vocal output in multi-talker situations", Journal of the Acoustical Society of America, 123, (2008), 803-813.

[6]      Barron, M, "Auditorium Acoustics and Architectural design", London, E&FN Spon, 1993.

[7]      Nijs, L, P. Versteeg, M. van der Voorden, "The combination of absorbing materials and room shapes to reduce noise levels", 18th International Congres on Acoustics, Kyoto (2004).

[8]      Nijs, L, "The Distribution of Absorption Materials in a rectangular room", Internoise , Rio de Janeiro (2005). This paper can also be found in web page "F. Artikelen".

[9]      See note 8



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