Room fashion

Raummode (from English room mode , there from Latin modus ; plural: Raummoden ) is a technical term in acoustics . It describes the properties of standing sound waves with a natural frequency in closed rooms, whereby the effect on the hearing impression of the people in them is of particular interest.

Room fashions between two hard walls. There must always be maximum sound pressure on the walls , which can be seen from the pressure bellies there.

A room mode is a natural shape of the air that fills the room while it oscillates at one of several natural frequencies. The oscillation oscillates between two opposing states of deflection . The room modes thus show where in the room vibration nodes and antinodes develop at certain natural frequencies.

For the observation period, the wave no longer travels through space, but has fixed amplitude maxima and minima. The nodes are zero points of the amplitude, i. H. there is no deflection at the point where a lump occurs. In practice this means that z. B. for living rooms with hi-fi systems, the hearing impression changes with the position of the person in the room. Depending on the room acoustics , some living room modes develop in the low frequency range , especially with normal living room dimensions, which can be very disruptive. Of primary importance are those fashions that are most developed. In rooms there are six degrees of freedom for natural vibrations , resulting in a multi-dimensional composition of the possible natural frequencies and their waveforms.

In principle, the number of maximum possible degrees of freedom is reduced again by the prevailing constraints . If the integer harmonics are excluded, there is a natural oscillation for each degree of freedom. The degrees of freedom for modes in spaces can be limited to three as a good approximation for calculations.

Stimulation of eigenmodes

While small rooms have extremely discrete natural frequencies, in large rooms such as churches all modes overlap to form a continuum - reverb occurs more intensely . In rooms, the room modes reflect how the sound of a room is discolored because certain tones are particularly prominent and have an uneven distribution of energy within the room. If discrete resonance frequencies occur, these are more noticeable than if several resonances are evenly distributed in the spectrum .

A certain resonance frequency distribution is a physical property of the room that depends on its dimensions. Only certain frequencies are excited. Both the increased level and the duration of the sound play a role in these resonance effects . The amplitude of an acoustic mode depends on its position in space. The degree of coloration of the sound therefore differs from place to place.

A standing wave. At the ends (the room boundaries) a pressure belly appears as a maximum.

Schröder frequency

If you know the reverberation time of a room (in seconds) and its volume (in ), the Schröder frequency or large room frequency can be determined with the help of the following numerical value equation , which is around 300 Hz in most rooms: ${\displaystyle T}$ ${\displaystyle V}$ ${\displaystyle \mathrm {m^{3}} }$ ${\displaystyle f_{\text{s}}}$

${\displaystyle f_{\text{s}}=2000\,{\sqrt {\frac {\text{T}}{\text{V}}}}{\text{Hz}}\approx {\frac {1}{\pi }}{\sqrt {\frac {c_{S}^{3}{T}}{V}}}={\frac {c_{S}}{r_{H}\pi }}}$

Almost the same results if one uses the speed of sound c _S or the Hall radius r _H and divides the result by π.

Below the Schröder frequency, acoustic modes of the room can cause perceptible coloration of the sound. Since these particularly affect the lower tones, they are perceived as droning , booming or one-note bass . Above, however, they do not cause any audible distortion of the reproduction in living rooms because the modes merge into one another in the form of dense reflections and reverberation.

calculation

Three types of standing modes that occur in a typical cuboid listening room are primarily calculated . These are axial (longitudinal), tangential and diagonal modes (also called obligue or oblique modes). The axial modes clearly dominate.

“The first-order spatial mode occurs at a frequency whose half wavelength corresponds to the distance between the two walls. [...] The natural frequencies of the one-dimensional space enclosed by the pair of walls under consideration is calculated from ${\displaystyle f_{\text{n}}}$

${\displaystyle f_{\text{n}}={\frac {c_{0}\cdot n}{2\cdot d}}}$

It is

• ${\displaystyle c_{0}}$the speed of sound ,
• ${\displaystyle d}$ the distance between the two walls and
• ${\displaystyle n}$ the order of the room mode, which at the same time corresponds to the number of sound pressure minima [...].

The considerations made on two parallel walls can be transferred to three-dimensional cuboid rooms. In addition to the modes described as being axial, there are also modes between two opposing wall pairs, the paths of which move in two and three dimensions of space. These are called tangential modes in the two-dimensional case and oblique modes in the three-dimensional case.

The calculation of all natural frequencies of a cuboid room can be done with the formula described by John William Strutt, 3rd Baron Rayleigh in 1896 : ${\displaystyle f_{\mathrm {n_{x}/n_{y}/n_{z}} }}$

${\displaystyle f_{\mathrm {n_{x}/n_{y}/n_{z}} }={\frac {c_{0}}{2}}{\sqrt {\left({\frac {n_{\text{x}}}{l_{\text{x}}}}\right)^{2}+\left({\frac {n_{\text{y}}}{l_{\text{y}}}}\right)^{2}+\left({\frac {n_{\text{z}}}{l_{\text{z}}}}\right)^{2}}}\,}$

It is

• again the speed of sound, ${\displaystyle c_{0}}$
• ${\displaystyle l_{\text{x}},l_{\text{y}}}$and are the dimensions of the room, i.e. length, width and height, and ${\displaystyle l_{\text{z}}}$
• ${\displaystyle n_{\text{x}},n_{\text{y}}}$and denote the orders of the modes in the respective directions. [...] ${\displaystyle n_{\text{z}}}$

The spatial sound pressure - sound velocity - distribution and thus the three-dimensional field of complex sound field impedances is composed of the superposition of all modes of a room . Room modes are systems capable of resonance. "( Stefan Weinzierl )

Atomic number

The frequencies and natural modes of vibration are named after their ordinal number, i.e.:

1. The first natural oscillation form or basic form occurs with an oscillation with the first natural frequency, the basic frequency .
2. The second natural mode oscillates with the second natural frequency.
3. etc.

If the composition of the natural frequencies is more complex, for example in rooms, the ordinal number is given in brackets with multiple digits or separated by commas.

Minimizing the impact

A room with hard walls shows distinctive peaks at certain room resonance frequencies. This can be changed by taking sound absorption measures . Depending on the amount and position of the absorbent materials in a room, these distinctive features are reduced. There is now a variety of acoustic absorber materials that are suitable for preferentially attenuating certain frequency ranges. Micro-perforated ceiling panels, special foils with perforations and conventional absorber panels can be used or combined to optimize room acoustics for the respective area of ​​application.

"For suspension heights between 200 and 600 mm, as they often occur in practice, the maximum effectiveness of this new type of acoustic ceiling is in the all-important frequency range between 125 and 500 Hz, where the ceiling's sound absorption is achieved with today's sparse furniture with consistently reverberant surfaces is urgently needed. At frequencies between 500 and 2000 Hz, where the ceiling swallows less, there is generally sound absorption by carpets, curtains and the people themselves. This leads to a relatively balanced reverberation time over frequency and a lower sound level in the rooms. "

Passive and active resonance absorbers are also used. If it is possible to change the room geometry in the planning phase, favorable proportions can be achieved. In combination with suitable sound reduction indicators, the room acoustics can be further optimized for the area of ​​application. The type of wall construction also has an impact on the room acoustics; lightweight construction usually means that there is less need for additional measures. However, carpeting or heavy curtains change the room acoustics to an area that should not necessarily be dampened. These have almost no influence on deep room modes that lead to the roar of the room.

Sound systems

Some providers have been offering complex so-called room correction systems with measurement microphones since 1990 and use current digital filtering options to implement the necessary compensation for room modes. Given the high cost of these systems, there is controversy about the relative value of improvement in normal rooms. Optimal use requires the operator to have a basic knowledge of the acoustic interrelationships and extensive data acquisition at the installation site, which must be carried out automatically in the device setting phase. The compensation and equalization via the frequency response of the sound system used are of limited use, since temporal processes are not influenced, such as the reverberation time and transient processes. The equalization is only suitable for a certain listening position and, if used incorrectly, can even worsen other listening positions. Neither the loudspeaker nor the measuring microphone may be placed in a node, because the acoustically induced cancellation of a frequency cannot be compensated for by increasing the amplification of the same frequency. Such an overcompensation would overdrive the loudspeakers without any appreciable benefit. Room correction systems record the actual frequency response at the measurement location, the user can usually select a target curve or design it himself, and the correction system generates an equalization curve that is intended to compensate for the difference between target curve and measurement curve. The design of the target curve requires knowledge and attention to local conditions; a straight-line frequency response specification used for simplicity would be a typical beginner's mistake. Even if a loudspeaker measured in an anechoic room still showed a linear frequency response, in practical use in rooms, in addition to room resonances, reflections on the floor, ceiling and side walls are to be expected, which arrive with a time delay. The resulting measured frequency response can no longer be linear because the time window for the measurement must be large enough not to rule out the build-up of room resonances. An alternative compromise is to suppress the known room resonance frequencies as completely as possible by using digital comb filters or notch filters when illuminating the room. Another possibility is to increase the number of woofers and amplifier channels and to control them in phase opposition at the affected resonance frequencies by means of complex digital processing, taking into account the signal propagation times through the room, and thus to partially cancel out reflections, whereby the location of the loudspeakers in the room is particularly important Meaning is. This partially improves the reproduction in larger rooms and neglecting the room modes in tangential and diagonal alignment.

See also

• Normal oscillation
• Shunt impedance

literature

• J. Krüger, M. Leitner, P. Leistner: PC instruments for measuring and testing acoustic parameters . In: IBP communication . tape 331 , no. 25 , 1998 ( fraunhofer.de [PDF]).
• HV Fuchs, C. Häusler, X. Zha: Small holes, big effect. In: drywall acoustics. 14, No. 8, 1997, pp. 34-37.
• HV Fuchs, M. Möser: Sound absorbers. In: Gerhard Müller: Taschenbuch Der Technischen Akustik. Springer, 2003, ISBN 3-540-41242-5 , p. 247 ( limited preview in the Google book search).
• H. Kuttruff, E. Mommertz: Room acoustics. In: Gerhard Müller: Taschenbuch Der Technischen Akustik. Springer, 2003, ISBN 3-540-41242-5 , p. 331 ( limited preview in Google book search).

Web links

• Spatial eigenmode calculator. For rectangular rooms, this calculator determines the room eigenmodes with the 20 lowest natural frequencies and displays them in ascending order.
• Calculation of the three room modes of rectangular rooms (standing wave calculation)
• Comprehensive room mode calculator (3D view of the pressure distribution of each mode, audio playback, Bonello diagram, bolt area, Schröder frequency depending on the reverberation time, etc.)
• The difference between the modes as sound pressure distribution in rooms and the modes of string vibrations
• Procedure for room acoustics analysis - practical instructions for determining room acoustics
• Simulation of the excitation of small rooms at low frequencies, IBP, Fraunhofer Institute Building Physics ( Memento from August 11, 2011 in the Internet Archive )

Individual evidence

1. ^ Thomas Görne: Sound engineering. 2008, ISBN 3-446-41591-2 , p. 72 ( limited preview in Google book search).
2. ^ Stefan Weinzierl: Manual of audio technology. 2008, ISBN 3-540-34300-8 , pp. 284–285 ( limited preview in Google book search).
3. ↑ Room acoustics, research direction: "Micro-perforated metal cassettes as a false ceiling". ( Memento from October 21, 2012 in the Internet Archive ) Fraunhofer Institute for Building Physics:
4. ↑ Suitable room dimensions. Retrieved March 27, 2020 .