The first thing to determine in the system is the amount of loss due to distance. For the purpose of our example, let’s assume that the furthest distance a listener will be from the speaker is 80 feet. Because sound radiates spherically, the attenuation is proportional to the square of the distance from the source, and thus there is a 6dB reduction for each doubling of distance. Assuming that the sensitivity of the loudspeaker is given in reference to 1 meter, this can be represented mathematically by the equation:

(1) SPLdist-loss = 20 log (distance in feet / 3.3)

The 3.3 factor is used to convert feet to meters. Using this equation, we determine there will be a total loss of 28dB as a result of distance. We can now calculate the maximum output level of the speaker that we will require in order to achieve our design criteria.

We have already determined that we need a maximum SPL level of 111dB at the listener position (101dB peaks with 10dB of headroom). At the loudspeaker we will need a maximum SPL level of 139dB (111dB at the listener position + 28dB of loss due to distance.)

The selection of the loudspeaker is the next step in the process. Any loudspeaker that is specified will have a sensitivity and a maximum power rating. The sensitivity is normally given in dB SPL at 1 meter when a 1-watt signal is applied to the input of the loudspeaker, and is usually given in AES watts.

This AES measurement is a clearly defined standard in which a band of pink noise from 125Hz to 8Khz, with +6dB peaks, is applied to the input of the loudspeaker for a period of two hours. Any loudspeaker that has its power rating in AES watts can very easily handle short-term peaks of +6dB above the AES rating.

The maximum output level at 1 meter away from a loudspeaker will be derived from the formula:

(2) SPLmax-AES = sensitivity + 10 log (AES power rating)

(3) SPLmax = sensitivity + 10 log (AES power rating) + 6

Any loudspeaker we select must have an SPLmax of at least 139dB. We will take one particular manufacturer’s loudspeaker that has a sensitivity of 112dB at 1 watt/1 meter. The high frequency component can handle 200 watts, AES. Using equation 3 (above), we find that the SPLmax equals 141dB. This loudspeaker will have the ability of achieving our design criteria.

To complete the design, we must choose the correct amplifier size for the application. Amplifier power ratings are given in watts, but unlike loudspeaker AES power ratings, amplifier power ratings are the upper limits and do not include any crest factors.