Potential Acoustic Gain

For a simple sound reinforcement system where the sound is assumed to drop off according to the inverse square law and the microphones and speakers are assumed to be omnidirectional, then the maximum achievable gain is determined by strictly geometric considerations. This simple case provides the framework for assessing what can be done in a real auditorium to increase the possible gain before feedback takes control.

Developing the Potential Acoustic Gain Expression

The maximum amplified level at the listener is 听众处的最大放大电平 Show 显示 so the maximum gain in decibels is 因此，最大增益以分贝为单位是 and bringing out the exponent gives 并带出指数得到

Calculate 计算

P.A.G. Expression Development

According to the inverse square law, the sound intensity at the listener without amplification is 根据反平方定律，未经放大时听众处的声强是 and level at the listener which corresponds to giving a feedback level equal to the input is shown below. 并显示了听众处的电平，该电平对应于提供等于输入的反馈电平。

This inverse square law expression gives the level at the listener if the loudspeaker is returning exactly the same level IM to the microphone that was originally produced at the microphone by the sound source. That is, it is returning exactly as much as it got as input so that there is a closed loop of signal returning to the microphone. 这个反平方定律表达式给出了当扬声器将恰好与麦克风最初接收到的相同电平IM返回给麦克风时，听众处的电平。也就是说，它返回的信号量恰好等于输入的信号量，从而形成一个信号闭环返回到麦克风。

The ratio of these two levels is the maximum gain before reaching the feedback condition. This ratio is used to develop the P.A.G. expression. 这两个能级的比值是在达到反馈条件前的最大增益。这个比值用于推导P.A.G.表达式。

Potential Acoustic Gain Calculation

For distance values 对于距离值 DS =m=ft D S = m= ft（专名或术语） 中文译文中的待填/计算数值依次对应：1：ds 2：dsc。实际数值以上方原输入框为准。 D1 =m=ft D 1 = m= ft（专名或术语） 中文译文中的待填/计算数值依次对应：1：d1 2：d1c。实际数值以上方原输入框为准。 D0 =m=ft D 0 = m= ft（专名或术语） 中文译文中的待填/计算数值依次对应：1：d0 2：d0c。实际数值以上方原输入框为准。 D2 =m=ft D 2 = m= ft（专名或术语） 中文译文中的待填/计算数值依次对应：1：d2 2：d2c。实际数值以上方原输入框为准。

= dB

You may enter values for the relevant distances in the simplified sound amplification system. Unspecified values will default to the values in the example model. You can change any values to convince yourself that the P.A.G. can be increased by increasing the distance from microphone to loudspeaker. The gain can also be increased by decreasing the distance from loudspeaker to listener or the distance from the source to the microphone.