Analysis of results
The microphone output voltage V is proportional to the instantaneous pressure. The sound pressure level (SPL), which is required for calculating reverberation time, is given by
SPL = 20log(prms/p0rms) and is expressed in decibels (dB)
In this definition, prms is the rms acoustic pressure and p0rms the RMS reference pressure for SPL measurements namely 2 x 10-5 N/m2
The reverberation time, by definition, is the time taken for the SPL to fall 60 dB. If the decay of the sound pressure is assumed to be exponential so that the SPL falls in a linear fashion, it is a simple matter to show that the slope of the graph of the SPL plotted as a function of time is just –60/RT.
The measured quantity is the microphone voltage rather than the actual sound pressure but the proportionality between these two quantities implies that a 60 dB fall in microphone voltage corresponds to a 60 dB fall in SPL so that the reverberation time can be calculated from the voltage measurements.
The procedure is to calculate the rms voltage Vrms and to find the slope of the graph of the logarithm of Vrmsplotted against time. In this case the slope of the graph is –3/RT.
The calculation of the rms voltage involves squaring each sample, averaging over a suitable time interval and then finding the square root of the average. Calculation of the reverberation time then requires the calculation of the logarithm of each rms voltage and a regression analysis to find the slope of the graph of log Vrms against time. Clearly in view of the large number of samples it is impossible to process the data by hand. The procedure adopted here is to use Picolog to save the data as a text file and then to import the data into a suitable program with facilities for data analysis. MathCAD is particularly suitable for this although Excel could also be used.
The output from a MathCAD document is shown in Figure 2. This shows the rms voltages computed within the document plotted on a logarithmic graph as functions of time and the regression line, also computed within the document, is superimposed.
The averaging time is a variable parameter of the calculation. For the graph shown here an averaging time of 200 samples or 10 ms was used The reverberation time calculated from the slope of the regression line is 1.44 s.
Figure 2: graph showing the decay of the rms voltage and the least squares regression line