Modeling Reverberation Time

One way to estimate the reverberation time of a room is to make a plot of the decay pattern from a sharp sound and approximate it with an exponential. The standard reverberation time is the time to drop 60 decibels, or to one-millionth or 10^-6 of the original level. If that time can be projected from the exponential decay, we have an estimate of the reverberation time of the room.

估算房间的混响时间的一种方法是绘制一个尖锐声音的衰减模式图，并将其近似为指数衰减。标准的混响时间是声音衰减60分贝，或衰减到原电平的百万分之一（10^-6）所需的时间。如果可以从指数衰减中投影出这个时间，我们就得到了房间的混响时间估计值。

对两边取自然对数得到：

Having evaluated the constant a, the expressions can be rearranged to give an expression for the reverberation time T:

在确定了常数a之后，可以将表达式重新排列，得到混响时间T的表达式：

If a voltage proportional to the sound amplitude is being measured with a microphone, then in terms of the measured voltages the expression for reverberation time T is:

The last step makes use of the fact that the sound intensity is proportional to the square of the amplitude of the wave, and that most microphones produce an output voltage which is proportional to the amplitude of the pressure wave. Since ln(x²) = 2ln(x), the constant a is divided by 2.

最后一步利用了声强与波振幅平方成正比的事实，以及大多数麦克风产生的输出电压与压力波振幅成正比。由于ln(x²) = 2ln(x)，常数a被除以2。

Above is an example of data from a handclap. There are lots of "real world" problems with this approach, and the only thing that can really be claimed is that it gives a real impression of the nature of sound decay in a room. The decay envelope is not symmetric about the horizontal axis, it is not a smooth decay, etc. The equipment used was just a microphone connected to a laptop computer and the software MacScope II from Elisha Huggins which gave an oscilloscope-type display of the microphone output as a function of time.

上面是一个手拍产生的数据示例。这种方法存在许多“现实世界”中的问题，唯一可以真正声称的是它能真实地反映出房间中声音衰减的性质。衰减包络线并不是关于水平轴对称的，也不是一种平滑的衰减，等等。所使用的设备只是连接到笔记本电脑上的麦克风，以及来自Elisha Huggins的软件MacScope II，该软件能够将麦克风的输出作为时间函数显示为示波器类型的图形。

如果用麦克风测量与声音振幅成正比的电压，那么在考虑测量电压的情况下，混响时间T的表达式为：

Reverberation Time Estimate