The influence of the room and the loudspeaker’s capacity rating
Acoustic room characteristics influence on the frequency characteristics of the sound pressure and also on the reproduction quality where there is realized acoustic reproduction. The same equipment will sound differently in different rooms. Acoustic features include: a form of a room, its volume and the sound absorption coefficients enclosing the room surfaces (ceiling, floor and walls). For example, curtains, carpets and upholstered furniture have a great sound absorption while the smooth ceiling and walls absorb sound little and reverb sound significantly. The open window is the perfect sound absorber. Sound absorption A is proportioned to the square absorber S and its sound absorption coefficient a
Every room (hall, lecture hall and room) has a rather difficult acoustic system with a resonant frequencies row. There are appeared air resonance oscillations inside of the room by any sound excitation containing the same frequency components. This effect leads to sound amplifying of these frequencies and changing sound signal spectrum.
Standing waves in the room strongly break the uniformity of the sound field as there are appear places with the maximum and minimum acoustic pressure (anti-nodes and nodes). Standing waves are formed not only between the pairs of parallel surfaces that are bounding the room but also in other combinations occurring in obliquity directions of sound waves distribution.
However the first type of oscillation (axial modes) is more effective in sound field forming of a room, especially of small size. The first (axial) frequency oscillation that occurs between parallel surfaces is fp1=168/l, Hz where l is the distance between limiting surfaces, m.
Harmonic components of this frequency will be multiple to 2, 3, etc. fold. Thus, the lowest frequency oscillation is determined by the largest size of the room. For example, free-running frequency between the walls in the biggest distance of about 3.4 m is 50 Hz. The most unfortunate shape for listening is a room of a cube form as it will have the same main resonance frequency and multiple frequencies (harmonics) in all three directions. So there are many free-running oscillations in any room while in the area of starting the lowest free-running frequency. Spectrum density of free-running oscillations is relatively small but rapidly increasing with the rising frequency. Therefore the spectrum density of free-running oscillations is so high that the resonance condition is low-observable starting from the 150-200 Hz frequency for not very small rooms. A large room is more conducive for sound reproduction as its main resonance frequencies decrease and overrun the working frequency range with increasing the size. And harmonics are forming almost constant spectrum and do not emphasize the sounds of separate frequencies due to their big number. It is desirable that the housing capacity will be not less than 42 m3 and one of the linear dimensions will be not less than 5 m where there is sound reproduction.
Effective resource for improving listening is the sound absorbers in the room that reduce the reverberation time. There are used sound absorbers which cover the ceiling and upper walls in the theaters, cinemas and concert halls.
At home the sound is absorbed by soft things including furniture. Listeners are also sound absorbers and the room absorption degree depends of its number. A suitable room for home monaural listening has reverberation time of 0.7 – 09 sec (for stereophonic listening – 0.4 – 0.5 sec).The more the airspace, the more can be a reverberation time while keeping good conditions for sound reproduction. On the diagram 28 is represented dependence of the most advantageous (optimal) reverberation time of the room from its size. On the diagram 29 there are represented frequency characteristics of the same high-quality loudspeaker that are measured in the room or sound measuring room for visual representation sound pressure dependence generated by a loudspeaker in the room. As we can see characteristic is unequal at frequency below than 400 Hz in a typical room (dotted line) while characteristics (solid line) is smoothed in the sound measuring room where all the defending surfaces have a big coefficient of sound absorption.
Frequency response type is highly dependent of microphone or loudspeaker location. On the diagram 30 there are represented frequency characteristics of the loudspeaker vented enclosure, measured in the lowest frequency in the open space which matches all conditions of sound measuring room 1, in the living room near a wall 2 and 3 in the corner. The figure shows that this area increases the sound pressure level, to develop ¬ direct speaker, and installing it in a corner of the room by radiation the lower frequencies by about 4 dB.
Diagram 28. Dependence of the optimum reverberation time of space from its size
Diagram 29. The frequency characteristics of the loud speaker that were taken in ordinary room (dotted line) and in a sound measuring room (solid line). In vertical axis there are represented the values of sound pressure level in decibels.
Diagram 30. The dependence of sound pressure level (dB) that is developed by the loudspeaker in the lowest frequencies from its location place
1 – in open air; 2 – near the wall in a room; 3 – in the corner.
Loudspeaker selection should start with a nominal power definition which will indicate power rating of low frequency power amplifier together with the output efficiency.
Nominal power of a loudspeaker should provide reproducing without overloading and appreciable increasing distortions, peak levels of the loud transmission types. Peak levels at 6-9.5 dB exceed the root mean square (effective) of the transmission level. Sound-reproducing equipment can be made with some margin of power. However, a significant capacity overestimation of the sound system (amplifier and loudspeakers) leads to its appreciation and especially to the increasing of service cost.
The greater the size of a room where operates sound-reproducing system, and high volume level will set for listening, the greater should be the nominal power of the system. Besides the space size amplifier’s power depends on the output efficiency of using loudspeakers, as well as the average coefficient of the room acoustic absorption. In calculating it is adopted the optimal reverberation time which it turns out the best sound.
If we assumed a uniform distribution of the sound energy density into the room, the total acoustic power of the sound source would be expressed with the formula
where p is the rms value of the sound pressure, Dyn/cm2; A-full sound absorption in the room, evaluated with the square of ideal sound absorber (open window), cm2; air density is equal to 0.0012 g/cm3; c-sound speed that is equal to 344 * 102 cm / sec.
A total sound absorption of the room A is related with its volume VP and the reverberation time T.
Substituting in the formula acquainted data for the acoustic power, the expression for A, and expressing power in watts, we will get:
In order to determine the required nominal power rating of the loudspeaker and power amplifier we enter loudspeaker’s output efficiency into this formula, then the final design formula for determining the electrical power of an amplifier and loudspeakers will be:
There are represented estimated nomograms in four oblique lines on the diagram 31 for better convenience. It can be found suitable electrical power of a power amplifier and loudspeakers that are required for space sounding of 20-300 m3 size. To calculate electrical power nomograms are made for two levels of sound reproducing that are conforming to sound of big orchestra of 75 persons with a sound pressure level of 96 dB ( effective sound pressure 1.25 N/m2) and orchestra of 18 persons with a level of 86 dB (effective sound pressure 0, 4 N/m2). Due to the fact that the peak sound pressure level is higher in 2 - 3 times than effective, the nomogram calculation is performed for both possible peaks.
Diagram 31. Nomogramsfor loudspeaker and amplifier power calculation depending on the space size and the intensity sound level.
1, 2 – for sound intensity level ( a big orchestra (75 persons); 3, 4 – for sound intensity level of small orchestra (18 persons).
The optimal reverberation time for rooms of different sizes is shown in a Diagram 28. The coefficient of loudspeaker efficiency set equal to 1% (N = 0, 01). This value can be guaranteed for many types of manufacturing loudspeakers but probably some of them (more powerful) have a little more output efficiency. Using the best loudspeakers in sound reproducing in customary calculation will form power margin.
Diagram 32. Relative power dependence of low and high frequency heads from frequency range.
Depending on a space size and the desired sound reproducing level (18 or 75 person orchestra), the required loudspeaker power will be situated between two inclined lines related to the sound intensity levels and conforming to a big or small orchestra.
The lower line in each pair (2 and 4) indicates the minimum required power as it relates to the double values of sound pressure at peak transmissions (levels of sound intensity are 92 and 102 dB) and they are four times the reserve capacity. The top line (1 and 3) indicates the maximum required power as it relates to the triple values of sound pressure at peak transmissions (95.5 and 105.5 dB levels) and is conforming to nine-fold power reserve. For example, to reproduce sound in a 51 m3 room (17 m2 square and 3 m high) at the sound intensity level that conforms to the big orchestra, we need loudspeaker and power amplifier from 3.7 to 8.3 W.
In a case, if a reverberation time is less optimal in the room sound intensity level would be less. It can be estimated the impact of sound absorption increasing in the room and an appropriate reverberation time decrease by opening a window in time of loudspeakers sound. The calculated power ratio relates to the wide-range loudspeaker. If it is used a two or three-way system, the power of low-frequency and radio-frequency heads could be determined by the curves of a Diagram 32 that are built according to the data of current power distribution of low and high frequency filters. Narrow band power is determined by multiplying the broad-band loudspeaker power on the value of relative power indicated by the curves for the selected frequency section.