Critical Distance or Dc is the distance from a sound source where the level of direct sound equals that of any reverberant sound. Dc applies to all sound gathering but measuring it is normally only required when advance planning of microphone positions is needed. Critical Distance does not dictate where a microphone must be placed but it does give a useful prediction of how it will sound at any particular point. For gathered sound to be reasonably “tight” and to have good intelligibility the microphone needs to be closer than Dc. Beyond Dc all sound will essentially be from the reverberant field, and will therefore be unsuitable for clear speech or sung words but ideal for atmosphere.
Critical distance can be measured with fairly basic tools. All you need is a broad spectrum sound source (“noise”) and a meter that indicates sound levels. That may sound technically complex but a “broad spectrum sound source” can be an ordinary FM radio tuned to the gaps between stations and the “sound level meter” an omni microphone and the meter on a portable mixer. These tools are quite adequate in practical terms.
Reverberant sound is essentially the same at any point in a space since it is reflected randomly off all surfaces. Therefore walk around the space with a sound meter and the levels measured hardly change. Direct sound obeys an inverse square law drop in level with distance i.e – 6 dB for every doubling in distance.
So set your noise source running and measure the level at distances of 10, 20, 40, 80… cm (or inches or handspans, it doesn’t matter). Initially there will be a drop in level of 4 – 6 dB (this is the real world) between measurements. At some point the drop from the previous reading levels off as you move into the purely reverberant field. That point is at the Dc.
Critical distance is fairly constant for anywhere within a space – the only caveat being that highly reflective surfaces like windows may need to be treated as direct sources since the sound bounced off them is not truly reverberant.
Measure the Dc on a recce and then draw a circle at that distance around the orch., singers etc on a floor plan. All mics intended to pick up primarily direct sound have to be within that circle. Note that we are really talking about a 3 dimension space not a 2 dimensional plan; the real shape is a sphere centered on the orch., singers etc. Omni microphones have to be positioned at <30% of Dc, cardioids at <50% and progressively more directional microphones can approach the boundary more closely. Outside that boundary the sound from the microphones will be reverberant and extremely “open”; inside the sphere is the region where acceptably “tight” sound is possible.
There is an online Critical Distance Calculator. This is intended to be applied to the reverse situation – loudspeakers for PA and the intelligibility of such systems – but the acoustic principles and the measurement do not change. Do not pay much attention to the implied precision of the results; 9 decimal places is rather silly in this context.