Room acoustics and physics - Department of Media Technology

Destructive interference from the seats: The seat-dip effect

2013-01-09T14:43:24+02:00

The seat-dip effect attenuates low frequencies of the direct sound and early lateral reflections due to the sound passing at near grazing incidence over audience seating. The seat-dip effect includes several phenomena due to the wave nature of sound, such as diffraction and scattering. The seat-dip effect has been studied in real concert halls [1-5], in scale models [1-3,5], via theoretical models [5,7], and wave-based modelling techniques [8-10].

The effect has been known for over 50 years. The main conclusions of the two fundamental articles [1,2] describing the effect are:

The rows of seats spread the low frequency sound energy in time, thus acting as a sound energy storing mechanism.
The frequency of maximum attenuation (typically between 100-300 Hz) depends on the height of the rows rather than on their spacing. The narrow band maximum attenuation is caused by a vertical resonance between the rows.
If the lower part of the seat is removed in order to create an underpass beneath the seats, the maximum resonant frequency is shifted upwards in frequency.
There is also considerable attenuation at a wider frequency range (up to 1 kHz), most probably due to the diffraction from the seat tops.
The attenuation does not depend markedly on the absoption of the seats. In addition, the attenuation hardly changes if the seats are occupied.

The attenuation can be reduced and shifted in frequency. For example, the main attenuation frequency decreases when the angle of incidence increases [3]. Thus, a high stage or an inclined audience area allow to tune the maximum attenuation to lower frequencies. In addition, adding Helmholtz resonators or vent boxes on the floor below the seats decrease the attenuation since they absorb a part of the sound that is delayed due to seat rows [4].

Simulation of the seat-dip effect with FDTD [10]

The concert hall is simulated with and without seating and floor in order to obtain only the direct sound with diffraction from the stage. Finally, the direct sound can be substracted from the original simulation to see the contribution of the seats. Consequently, modelling allows for the study of a single aspect of the seat-dip effect which is not possible with measurements only.

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Research on the seat-dip effect in Aalto

The study of the seat-dip effect is one of the modeling applications of the finite-difference time-domain methods developed by the Virtual Acoustics team. The modeling makes it possible to study the seat reflections without the presence of other reflections. Based on the modeling results, it is confirmed that the seat-dip effect rises from the delayed sound interfering destructively with the direct sound [10]. In addition, the delayed sound is shown to be directed upwards. Based on the analysis of six concert halls measured by the Virtual Acoustics team, the seat-dip attenuation is best corrected in halls that provide the most lateral reflections [6].

Perceptual evaluation of the seat-dip effect rather an undeveloped field, and the research in Aalto aims at unraveling this. The seat-dip effect is linked with the quality of sound in concert halls, and the effect seems in some cases to render the sound muddy, and to obscure the articulation of bass instruments [10].

References

[1] T. Schultz and B. Watters, “Propagation of sound across audience seating,” Journal of the Acoustical Society of America, vol. 36, no. 5, pp. 885–896, 1964.

[2] G. Sessler and J. West, “Sound transmission over theatre seats,” Journal of the Acoustical Society of America, vol. 36, no. 9, pp. 1725–1732, 1964.

[3] J. Bradley, “Some further investigations of the seat dip effect,” Journal of the Acoustical Society of America, vol. 90, no. 1, pp. 324–333, 1991.

[4] W. Davies and Y. Lam, “New attibutes of seat dip attenuation,” Applied Acoustics, vol. 41, no. 1, pp. 1–23, 1994.

[5] D. Takahashi, “Seat dip effect: The phenomena and mechanism,” Journal of the Acoustical Society of America, vol. 102, no. 3, pp. 1326–1334, 1997.

[6] J. Pätynen, S. Tervo, and T. Lokki, “Analysis of concert hall acoustics via visualisations of time-frequency and spatiotemporal responses,” Journal of the Acoustical Society of America, vol. 133, no. 2, pp. XX-XX, 2013.

[7] Y. Ando, M. Takaishi, and K. Tada, “Calculations of the sound transmission over theater seats and methods for its improvement in the low-frequency range,” Journal of the Acoustical Society of America, vol. 72, no. 2, pp. 443–448, 1982.

[8] J. LoVetri, D. Mardare, and G. Soulodre, “Modeling of the seat dip effect using the finite-difference time-domain method,” Journal of the Acoustical Society of America, vol. 100, no. 4, pp. 2204–2212, 1996.

[9] W. Davies and T. Cox, “Reducing seat dip attenuation,” Journal of the Acoustical Society of America, vol. 108, no. 5, pp. 443–448, 2000.

[10] T. Lokki, A. Southern, and L. Savioja, “Studies on seat dip effect with 3D FDTD modeling,” in Proceedings of Forum Acusticum, Aalborg, Denmark, 2011.

[11] W. Davies, T. Cox, and Y. Lam, “Subjective perception of seat dip attenuation,” Acta Acustica united with Acustica, vol. 82, pp. 784–792, 1996.

Acoustics of Epidaurus

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The capability of the ancient theatres to amplify speech has been fascinating researchers of acoustics for decades. Many different explanations have been proposed to explain why even at the back row speech is clear and well audible. The speech intelligibility is very high all over the huge audience area [1].

The most extensive, but unfortunately not very well known, study of the acoustics of the ancient theatres has been presented by Canac [2]. His book has in many aspects made a prominent contribution, especially considering that the book was published in the 1960s. He studied different geometries with image sources and showed how the direct sound and early reflections from the orchestra and the back wall of the stage are important to amplify the voices of ancient actors. Moreover, he proposed that sound waves might travel along the circular seating rows, i.e., by bending along the curved surfaces. However, he misunderstood the contribution of lateral reflections by proposing that they should be suppressed and he did not discuss the backscattering of sound from the seating rows at all.

Perhaps the most well-known explanation of the acoustics of ancient theatres has been published by Declercq and Dekeyser [3]. They performed acoustic simulations on an Epidaurus model using a geometric acoustic modelling method incorporating multiple orders of diffraction. They concluded that the sound is backscattered from the cavea to the audience making the audience receive sound, not only from the front, but also backscattered sound from behind. Thus Declercq and Dekeyser concluded that the seat rows act as a high-pass filter amplifying high frequencies more than low frequencies and the cross-over frequency of such filtering depends on the periodicity of seat rows, in Epidaurus it is around 500 Hz. However, the measurement results by Psarras et al. [4] do not support the findings with simulations of Declercq and Dekeyser. Frequency responses in Fig. 1 do not show any considerable attenuation of the frequencies below 500 Hz. Instead, the low frequencies below 150 Hz are emphasized, although at approximately 180 Hz the frequency responses contain a dip, probably due to the backscattered sound from the seating rows.

Figure 1: Measured frequency responses.

Frequency responses at positions R2, R5, R8, and R10, smoothed at 1/3 octave bands. Four responses are computed within a time window from the initial direct sound up to 20, 50, and 1000 ms.

Figure 2: Frequency responses of simulation results.

Frequency responses (smoothed at 1/3 octave bands) at receiver positions 1 to 31 on Line L from source position S4 on the stage. The average frequency response of male speech is shown for reference.

Figure 3: 3D model of the lower cavea of Epidaurus.

The model of Epidaurus used in the simulations. The model has only the lower cavea consisting of 31 seat rows. Source position S1 is in the center of orchestra and sources S2, S3, and S4 are on the stage. Simulations were done for 123 receiver positions.

Figure 4: Visualization of 2D simulation.

Visualization of 2D FDTD simulation at five different time moments.

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Our explanation on the acoustics of Epidaurus

We studied the acoustics of Epidaurus with 2D and 3D FDTD simulations [5]. The simulation results matched quite well to the measurements [4], in particular at low frequencies. Based on the analysis of the in-situ measurements, visits, and simulations, we explain the great acoustics for speech as follows.

The strong sound and high speech intelligibility requires high enough signal to noise ratio. Epidaurus is located at the peaceful countryside in Greece. Therefore, the background noise in the venue is considerably low and signal to noise ratio is reasonably high, in particular at ancient times when the stage building blocked the excess noise from the valley.

In addition to unobstructed direct sound, the early reflections are very important for good speech intelligibility [6]. The reflections from stage wall, orchestra, seating rows and backscattering of the seating rows arrive to the listener considerably fast after the direct sound. In addition, they are all from hard and reasonably flat surfaces, thus they are well fused to the direct sound, resulting in much stronger and louder sound [7]. The sound power in speech is carried by the vowels, which are harmonic signals. Figure 2 shows the comparison of the frequency responses from the stage to all seat rows with average spectrum of 10 s of anechoic male speech. Below 500 Hz, due to backscattering and early reflections, Epidaurus amplifies the power carrying frequencies for vowels in male speech, i.e., fundamental frequency F0 (125-140 Hz) and first harmonics (250-290 Hz and 375-420 Hz). The information in vowels is in three main formant regions. For all vowels they are between 300 and 3000 Hz, i.e., the highly amplified frequency region in Epidaurus due to backscattering from higher seating rows. The seating rows are 0.367 m high, i.e., effectively reflecting frequencies higher than f = 340 / (2*0.367) = 463 Hz (at least half of the wavelength).

The late reverberation is detrimental for speech intelligibility, because reverberation masks and blurs transients and consonants in speech. The Epidaurus has short late reverberation and it is at low level, mainly because the venue is not an enclosed space. Moreover, there is hardly any reverberation at low frequencies, which can be clearly heard from a video of an impulse response measurement see video. The video also reveals that when this impulse response measurement is listened to the orchestra area the Epidaurus clearly has a ringing sound on musical A note, i.e. 220 Hz and its harmonics (440, 660, 880, etc.). Indeed, the depth of one seat row is 0.746 m, thus f = 340 / (2*0.746) = 227 Hz and when the impulse has to diffract-reflect-diffract at higher seating rows the distance is a bit longer, resulting approximately 220 Hz. Again, this frequency matches well with the fundamentals in human speech. Similar tone color was heard all over the audience area during the impulse response measurements (when the video was shooted), although the ringing was considerable shorter.

To summarize, the early reflections fuse to direct sound and raise the overall sound power level. However, at low frequencies periodic seating rows filter out the frequencies with no excitation in speech, but amplify the fundamental and first harmonics of male speech, thus raising signal to noise ratio. In addition, there is hardly any late reverberation to muddy sound at low frequencies. At higher frequencies from 500 to 4000 Hz, the seating rows amplify considerably the sound, resulting in high speech intelligibility all over the audience area.

References

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Diffusing structures

2013-01-09T14:43:24+02:00

Diffusers are structures that have been specifically designed to scatter sound energy. They are used for example on back walls in large auditoria for preventing disturbing echoes and for reducing coloration due to standing waves in small sound reproduction rooms. There are a variety of different design principles for diffusers (number theoretic/Schroeder diffusers, optimized curved surfaces, fractals etc.), but generally all of them aim at fulfilling the same criterion: an ideal diffuser produces within its operational bandwidth a polar response that is invariant to the angle of incidence, angle of observation and frequency [1].

The diffusion coefficient [2] quantifies the degree of uniformity of the polar response of a surface and it has been developed to serve as a quality measure for diffusers. It is also useful for quantifying the diffusing properties of other surfaces, for example the layered wall structures found in some concert halls. These structures feature a panel with some form of openings or perforations and a back wall behind the panel. Typically structures of such description are known as Helmholtz absorbers or distributed Helmholtz resonators [3], that work on the principle of mass-spring resonance and absorptive material inside the cavity. However, when the area of the openings is greater and no absorptive material is present, the structures behave differently. These kind of structures are found in many concert halls, including the Helsinki Music Centre concert hall built in 2011, yet the principles of their design, application and effects are somewhat elusive.

Research on effects of layered wall structures

In our work, we have done 2-D FDTD simulations in order to examine the reflections from layered wall structures. These studies include the time- and frequency-domain effects and spatial diffusion [4][5]. The slatted panel is frequency-selective in reflecting and transmitting sound; low frequencies are mostly transmitted through and high frequencies are reflected. Additionally, the panel introduces a notch in the frequency response. Wider slats and thicker panel lower the notch frequency.

The panel coupled with a flat back wall creates a resonant system where the panel acts as a filter, and the cavity acts as a delay line. The overall reflected sound consists of multiple successive wavefronts, generated by the combination of delays imposed by the cavity depth, and the accumulated filtering by multiple interactions with the panel. In the frequency domain, this is a comb filter effect, due to the interference between the differently delayed wavefronts. The saw corrugated back wall makes the situation more complex, but the most prominent aspect of it is the added diffusion at wavelengths comparable to the dimensions of the corrugation.

2-D FDTD visualizations

Reflection responses from two layered structures with identical slatted panels and different back walls; flat back wall (left), saw corrugated back wall (right). [4]

Polar responses for slatted panel with saw corrugated back wall

Polar responses for a subset of 1/3 octave bands for 0° (first row), 20° (second row), 50° (third row) and 70° (bottom row) incidence angles; black lines = reference flat surface, red lines = slatted panel with saw corrugated back wall. [4]

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References

[1] T.J. Cox and P. D'Antonio. Acoustic Absorbers and Diffusers: theory, design and application. Taylor & Francis, second edition, 2009.

[2] AES-4id-2001. AES information document for room acoustics and sound reinforcement systems – characterization and measurement of surface scattering uniformity. JAES, 49:149-165, 2001.

[3] T. E. Vigran. Building Acoustics. Taylor & Francis, first edition, 2008.

[4] A. Haapaniemi. Simulation of acoustic wall reflections using the finite-difference time-domain method. (Master's Thesis), Aalto University School of Electrical Engineering, 2012.

[5] A. Haapaniemi, A. Southern, T. Lokki. A finite-difference time-domain investigation of reflections from layered wall structures. ISRA 2013.