Calculation of power capacity of sound box in studio

Studio sound reinforcement, like any other indoor sound reinforcement, there is a problem of determining the power capacity of the speaker used according to the sound pressure level of the sound reinforcement site, which is usually called electrical power. Although for a given room, the designer can determine the electrical power of the speaker he is familiar with according to experience, for an arbitrary room, a random speaker brand, it is not enough to rely on experience without scientific calculation. Because the electric power is too small, it will not reach the loudness, clarity and distortion degree. The power is too large, and will cause unnecessary waste. After all, the electric power of the speaker that meets the sound pressure level requirements of the sound reinforcement site is not only related to the sensitivity level of the speaker, directivity factor, directivity coefficient and other parameters, but also related to the peak factor of the sound field of the sound reinforcement and the room constant. Therefore, before the establishment of a new studio sound reinforcement system, it is necessary to carry out due calculation.
It should be noted that the following calculation method for the electrical power of the speaker is also suitable for outdoor sound reinforcement, except that the influence of the room constant is no longer included.

one A few basic concepts.
Before we get into the specific calculations, let's discuss the following:
1. Directivity factor, directivity factor and sensitivity level of the speaker.
(1) Directivity factor Q (d) : It represents the multiple of the sound intensity generated by the speaker at a certain point in space than the sound intensity generated by the theoretical non-directional speaker. In actual calculation, it is characterized by the vertical radiation Angle v and horizontal radiation Angle h of the speaker:
Q (d) =180O/sin-1[sin(v/2)·sin(h/2)]
In the formula, the units of v and h are degrees (O), and Q (d) has no dimension.
(2) directivity coefficient Q (θ) : It represents the sound pressure produced by the speaker at a point deviating from its radiation axis θ Angle, which is a multiple of the sound pressure attenuation at the same distance point. Q (θ) is given by the pointing characteristic pattern (or directional pattern) of the reference speaker in the following formula:
20 lg Q (θ) = L (θ) -L (a),
That is: Q (θ) =100.05[L(θ) -L (α)] formula, L(θ) is the sound pressure level of the measuring point that deviates from the axial θ Angle of the speaker, L(a) is the sound pressure level at the same distance from the measuring point in the axial direction.
(3) Sensitivity level Ls: sound pressure level generated at 1m in the axial direction of the speaker driven by 1w reference electric power (sound source is pink noise). The unit is dB spl.
It can be seen from this definition that if Ls is known, when you want to have a sound pressure level Lr of 90dB at the axial r (m) of the speaker, if you want to find the electrical power We of the speaker at this time, just convert Lr to the sound pressure level Lr 'at the axial 1m (when only considering the direct sound energy of the room and ignoring the mixed sound energy, there can be: Lr '= Lr+20 lg r), the power level difference between the electrical power We and the reference electrical power (lw) can be obtained from the sound pressure difference between Lr' and Ls, and then We can be obtained. In other words, since the difference between Lr 'and Ls is the difference between the sound pressure level generated by We and the sound pressure level generated by the reference electric power, there is the following quantitative relationship in calculation (note that it is not in physical concept) : Lr' -Ls=10 lg (We/lw)
I.e. 10 lgWe= Lr '-Ls or: We=100.1 (Lr' -Ls)
It should be noted that since the actual listening range cannot be only in one axis, We must also be related to Q (d), Q (θ) and the peak factor and room constant to be talked about below, and the above formula only gives an expression of the magnitude value of We in a simple case.