Voltage measurements to determine input power

According to the WinISD support notes, input power to a speaker can be determined by the following formula:
Input power = RMS voltage squared / DC resistance of coil

Voltage measurement should thus give an accurate means of determining input power, and in conjunction with modelling in WinISD, determining SPL and port velocity. This neatly bypasses any problems with room nodes that can occur if an SPL meter is used.
The approach was discussed with members of the diyAudio discussion forum, and with the WinISD support forum.

Reality Check

A test was done comparing SPL determined by voltage measurement, against SPL measured with an SPL meter.

An existing sub was measured at 30hz, outside, on the edge of a deck, with the acoustic centre 1.25m above ground, and the SPL meter 1m away. Simultaneous measurements of SPL and voltage were taken.

The SPL was 92dB, as measured with a Radio Shack SPL meter
Adding 3dB correction for the analog Radio Shack meter @30z, gives a measured SPL of 95dB

The voltage across the drivers was 11.5V RMS, measured with an analog multimeter.
The DC resistance of both drivers in series is 7ohms
Calculated Input power = RMS voltage squared / resistance = 18.9 watts
Put 18.9w into WinISD and read off SPL @ 30hz = 102dB

Test sub with 18.9w applied
WinISD model of test sub with 18.9w applied

To accurately specify the input power at 30hz, the modelling in WinISD is done without any amplifier boost factored in.
This SPL figure given by WinISD is for measurement in "half-space".
Since the test was done outside with the speaker 1.25m above the ground, and the meter 1m away, a "full-space" value for SPL is closer to what will be measured
To convert a "half-space" SPL to an equivalent "full-space" value, subtract 6dB.
This gives the SPL as determined from voltage measurement of 96dB

With the SPL being within 1dB for the two methods, we can see that voltage measurement is an acceptable method for determining input power and thus SPL



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