Relationship - Total RMS Sound Output and Total RMS Electrical Input

A GA to you! You've got the answer. If you take care with the impedances, you can cover a whole stadium with a 30 W amp that draws maybe 400 W input. Or, you can screw up the same coverage with a 600 W amp that draws maybe 1000 W input. Mmm? Methinks salesmen and marketers screw around with the specs.

Premium,

Is there any relationship between total RMS sound output and total RMS electrical input?

Yes.

Can I determine total electrical input (electrical power consumption) based on wattage RMS sound output?

No.

To measure the electrical characteristics you can put a sine wave tone on the input and put a resistive dummy load of the appropriate Ohmic value on the output and calculate the power on the load and compare it with the input power.

Recognizing that you asked about RMS sound power you would have to get some scientific equipment and an audio laboratory to play that game.

But as the man said: "owing to the wide range of acoustic efficiencies between various types of speakers, the sound octaves involved, etc."

Sound power levels are indicated in decibels.
Lw = 10 log (W / Wo)
where: The reference power is 10^-12 watts (W), which is the lowest sound persons of excellent hearing can discern. Sound power is measured as the total sound power emitted by a source in all directions in watts (joules per second).

Since sound measuring instruments respond to sound pressure the "decibel" is generally associated with sound pressure level (SPL). Sound pressure levels quantify in decibels the intensity of given sound sources. Sound pressure levels vary substantially with distance from the source, and also diminish as a result of intervening obstacles and barriers, air absorption, wind and other factors. Sound pressure levels are indicated in decibels.
Sound pressure level (SPL) Lp = 20 log (p / po),
where: The reference sound pressure is po = 2 x 10^-5 pascals.
The usual reference level po is 20 x 10^-6 pascals = 20 micropascals.
Sound pressure is a pressure disturbance in the air whose intensity is influenced not only by the strength of the source, but also by the surroundings and the distance from the source to the receiver. Sound pressure is what our ears hear and what sound pressure level meters (SPL meters) measure.

Kuduk

Yes to your question that out-put & power-input has ofcource relation.

The sound output [On speakers-consoles ratings is PMP i.e. Peak-Musical-Power not peak-power] can not be measured as it is not continuous wave but musical sound containg plses of different amplitude & frequencies.

RMS power can only be measured by a sine-wave input to Audio-amplifier [devices] from a function generator; normally measured on 1000 hz.

Note:

Look into the ratings given on a speaker used in units of rated 100W. You will be astonished to find it not better than 10W only.