The loudness of a sound we hear reflects the power of the wobbles in the air detected by our ears, which (if we can just sit still for a minute) is directly related to the power delivered by the loudspeaker(s).

Music can be stored in both analog and digital forms, but to get air moving in our ears an analog voltage has to be created, fed from the audio amplifier to the speakers. The voltage across the speaker terminals is proportional to the sound wave’s amplitude (the shift in position of the air). The amplitude that corresponds to the voltage is not the same as the loudness we hear. Power delivered by a loudspeaker is proportional to the square of the voltage delivered by the amplifier to its terminals (that is, the voltage multiplied by itself). That’s basic electricity that we can’t escape. Similarly, the loudness we hear is proportional to the square of the amplitude of the sound wave.

Suppose we have a sound in one speaker only. The speaker gets a voltage corresponding to the sound’s contribution to the recorded sound (and all such contributions add up to the whole record). When the resulting sound wave arrives at our ears, we hear a loudness corresponding to the square of that instrument’s voltage across the speaker terminals.Now let’s listen to the same sound at the same loudness in the middle of the stereo. To make it sound as loud as if it is in just one of them, each speaker contributes power so that the loudness at our ears is the same as with one speaker. Each speaker now gets a voltage slightly less than three quarters (0.7 times) of the one-speaker situation.

That means that when you square the contribution from each speaker’s voltage, you hear the same loudness as when the instrument was in just one speaker. But when you add two stereo channels to give just one mono, you add the voltages that are applied at the speakers. The power delivered to the air, and the loudness we hear, are still proportional to the square of the voltage at the speakers. We see that the voltage for our sound that lived in just one speaker is the same. But when you add the voltages that were across two speakers to give the same loudness, you find that they are greater, and the voltage is almost half as much again (1.4 times) as for one speaker.

When we square this to get the power of the air movement at our ears, and therefore the loudness we hear, we find the power of sounds at the center of the sound stage is exactly twice what it was when our noble sound started in just one speaker. So we hear it twice as loudly. That’s 3 dB in audio measurement terms. Very noticeable.