The basics of SPL
Currently, there is a trend towards larger dedicated rooms for home cinemas so that more members of the family can take part in the activity. This poses problems for the custom installer in recommending products that will create an authentic cinema experience, especially for the loud passages in movies.
Commercial cinemas have had their sound pressure levels (SPLs) well defined for decades; the reference level being 85dB SPL (-20dBFS) and the peak level 105dB SPL (0dBFS), measured at a point two-thirds back on the centre line. To maintain realism it would be desirable for home systems to approach these SPLs. However, there are some issues.
One is the maximum SPL obtainable from a loudspeaker. Because the loudspeakers are behind the screen in larger installations, high frequencies are muffled (attenuated) and even more SPL is needed.
ADVERTISEMENT
Another is the dispersion of the sound into the room and the effect of early reflections on the timbre.
The typical hi-fi loudspeaker runs out of steam trying to make enough SPL in larger home cinemas. Even if it could produce the required SPL, there would be high levels of distortion compared with a semi-pro loudspeaker. The latter’s higher initial sensitivity and greater power handling give it the advantage.
Typical loudspeakers also have irregular frequency responses in off-axis directions. This colours the timbre of early reflections from the floor, walls and ceiling, and thus the overall sound.
A semi-pro loudspeaker with a constant directivity (CD) horn has a tighter, more controlled dispersion pattern and more uniform off-axis frequency responses. Early reflections are less coloured and lower in SPL.
Sufficient care must be taken in the design and implementation to ensure suitable flat on-axis frequency responses.
MAXIMUM SPL
It is readily observable that the farther you are from a sound source the quieter it becomes: sound waves lose strength as they spread out like ripples in a pond.
In a room, reflections occur and the perceived SPL is slightly higher. However, for system design and calculation purposes, the direct sound is used. As explained in Technical Guidelines for Dolby Stereo Theatres (1994): “Transient sounds (of short duration) are not augmented by reverberation, and the required power for a given sound pressure level at a specific seat is controlled by the direct sound – an inverse square law characteristic based on how far the listener is from the loudspeaker.”
Some numbers can be put on the inverse square law.
Figure 1 shows the effect: doubling the distance reduces the SPL by 6dB. It is important to note that this applies in a free field, that is, no reflections or reverberation.
Loudspeaker systems usually have a specification, of which one aspect is the sensitivity – how much SPL for how much electrical input (in volts).
For example, a premium floorstanding model from Krix creates 90dB SPL when driven by 2.83V and measured at a distance of 1m. It would typically be used with amplifiers of 200W output.
Its maximum output can be calculated to be 113dB at 1m, reducing to 107dB at 2m, and 101dB at 4m. However, there would be very noticeable distortion under these conditions.
In practice, the loudspeaker drivers heat up considerably due to thermal power compression, reducing the SPL to 99dB at 4m.
Compare that with a semi-pro loudspeaker available from the same Australian manufacturer. A typical specification might be 97dB/2.83V/m with a 300W AES power rating.
Its maximum SPL can be calculated at 124+dB at 1m. This reduces to 118dB at 2m and 112dB at 4m, giving more than adequate headroom and lower distortion, even after a further reduction of 2-3dB due to thermal power compression. However, the systems wouldn’t be run that close to clipping, so the semi-pro loudspeaker system would sound much louder and cleaner than a domestic hi-fi loudspeaker at 4m.
DISPERSION OF SOUND
An often neglected aspect of loudspeaker systems is dispersion of sound.
The maximum SPLs calculated above were based on the direct sound (the first arrival), but in practice the early reflections augment the perception of sound pressure level.
But there is a catch. If the early reflections don’t have the same frequency response as the direct sound they will have a different timbre, thereby adding to and colouring the direct sound.
It is well known that at low frequencies loudspeaker drivers radiate omnidirectionally.
More technically, the radiation is omni-directional when the radiating area is small compared with the wavelength of the sound.
Less well known is that as frequency increases (and wavelength shortens) the dispersion narrows, until at frequencies where the wavelength is about the diameter of the cone/dome, the sound radiates in an approximate 90º cone shape.
Ideally, before that happens the loudspeaker driver should be crossed over to a smaller one so that the radiated sound preserves the beam angle as much as possible. This is one of the reasons a three-way loudspeaker system sounds different from a twoway loudspeaker system, even though they are both likely to have flat on-axis frequency responses.
A solution from pro sound is the CD horn. A well designed CD horn will maintain its dispersion to at least 10kHz, ie: minimal variation of the beam angles with frequency. Typical values would be 90º horizontal by 40º vertical. Then the early reflections will have the same colouration and there is minimal timbre change due to off-axis sound radiation.
The mouth size of the horn determines the lowest frequency at which it will hold its pattern control – the larger the lower.
Many horn-loaded loudspeaker systems have too small a horn mouth in relation to the low-frequency driver used, and there will be an abrupt change in dispersion, ie: beam angle at the crossover frequency.
Yet there are exceptions. For example, Krix has designed its own range of horns and, among other systems, have made a two-way system comprising a 15-inch (380mm) low-frequency loudspeaker and a high-frequency horn with a mouth about 330mm square.
The crossover frequency is about 1kHz, at which frequency the low-frequency driver and the horn have beam angles of about 90 by 90 – a good match.
The beam angle graph is shown in Figure 2 in a high-resolution graph of 1/10 octave. Apart from a dip in the vertical beam angle as an inevitable consequence of the crossover network, the dispersion (beam angles) at high frequencies is commendably uniform.
The directivity index (DI) is another important characteristic of loudspeaker systems is rarely shown. It can be considered as the ratio between the onaxis response and the power response, ie: the total sound energy radiated into the room in all directions. In short, the smoother the better.
Many two-way and three-way designs show significant ‘bumps’ in the DI, caused by each driver narrowing its dispersion (beam angle) and increasing the DI before crossing over to the next driver – wide dispersion, lower DI. The DI is shown in Figure 3 as a graph of the 1/10 octave. It is also commendably smooth. The effect of the crossover network can be seen in the 1kHz region. It is measured over the front hemisphere, so at low frequencies trends to +3dB rather than the 0dB expected of an omnidirectional source.
EXAMPLES OF MAXIMUM SPL CALCULATIONS
Now we get to number crunching. In the example of Krix’s premium floorstanding model, a voltage of 40V is clearly in excess of the 2.83V that makes 90dB SPL.
To find out what the increase represents in dB we need to use the formula dB = 20*log10(40/2.83), which works out to a 23dB increase. So presumably the loudspeaker system is producing 90+23=113dB at 1m. Not to worry, people don’t usually sit that close to the loudspeakers.
A bit more number crunching is needed. For hi-fi sized loudspeakers, at distances more than about 1m, the SPL of the direct sound drops off at approximately 6dB for a doubling of the distance. So our 113dB at 1m becomes about 107dB at 2m, and 101dB at 4m, a close listening distance for larger home cinemas.
Practically, you wouldn’t run the system that close to the maximum (clipping) level and would not achieve this SPL.
But this is not the end of the story. More number crunching is needed (sorry).
The SPL on loud passages is actually less than the stated figure, as the increase in voltage causes a big increase in power soaked up by the loudspeaker, thereby heating it up.
Consequently the electrical impedance increases, the loudspeaker absorbs less electrical power and there is reduced SPL on peaks. This is called thermal power compression, and all loudspeakers do it. You would lose another 2-3dB, resulting in an SPL on loud passages of less than 100dB.
Compare that with a semi-pro loudspeaker available from the same Australian manufacturer.
A typical specification might be 97dB/2.83V/m, and 300W AES power rating. Typically one can specify an amplifier of twice the thermal rating, so the peak voltage from a 600W amplifier would be 69V output. This represents an increase in dB of 20*log10(69/2.83), which works out to a 27.8dB increase, so the maximum SPL at 1m would be 97+27.8=124.8dB and at 4m you could expect 112dB.
Thermal power compression would lose another 2-3dB, resulting in an SPL on loud passages of just under 110dB at 4m. Again, in practice you wouldn’t run the system so close to the maximum (clipping) level. However, the loud passages of a movie would be very loud – and very clean.
-
ADVERTISEMENT
-
ADVERTISEMENT
-
ADVERTISEMENT
-
ADVERTISEMENT