Simplified Model: Sound Reinforcement

Assume*: Inverse square law dropoff of sound Omnidirectional loudspeakers and microphones

The loudspeaker provides more sound to the listener than would otherwise have been received, but it also produces sound at the location of the microphone. This feedback to the microphone limits the amount of amplification which can be used.

The microphone creates an electrical image of the sound which is amplified and used to drive a loudspeaker.

Numerical Example: Need for Amplification

By the inverse square law, a doubling of distance will drop the sound intensity to 1/4, corresponding to a drop of 6 decibels. Simplified sound system model

The following simplifying assumptions allow us to calculate the sound levels and assess the need for amplification: 1. The sound drops off according to the Inverse square law. 2. The microphones and loudspeakers are omnidirectional.

80 dB at 2 ft 74 dB at 4 ft 68 dB at 8 ft 62 dB at 16 ft 56 dB at 32 ft 50 dB at 64 ft 44 dB at 128 ft

Numerical Example: Need for Amplification

80 dB at 2 ft 74 dB at 4 ft 68 dB at 8 ft 62 dB at 16 ft 56 dB at 32 ft 50 dB at 64 ft 44 dB at 128 ft

Starting with 80 dB at two feet and using the fact that every doubling of distance will drop the level by 6 dB, we learn that a listener at 128 ft would receive a sound intensity of only 44 dB

Maximum Amplification Condition

When the feedback to the microphone is equal to the original sound input level, the gain can no longer be increased without an uncontrolled increase in output, usually in the form of a loud ring at one frequency. Practically, the sound should be kept about 3 dB below that point. If 80 dB is the input level to the microphone, then 80 dB feedback return is an upper bound. Using the inverse square law, the resulting levels are as shown.