Speaker sensitivity & amp power

ako

Member
Am I understanding this math correctly?

A 3dB increase in volume requires a doubling of Watts.

There is a 6dB loss in volume for every doubling of distance.

If I have a 99dB sensitivity speaker at 1 watt, 1 meter, and I want to know how many watts my power amp will need to deliver in order to be CAPABLE of achieving 105 dB at 4 meters, I would take the 99dB, reduce it by 6 at 2 meters, and another 6 at 4 meters. Now I have 87dB at 4 meters, and 1 watt. Climbing back up, I get to 90dB with 2 watts, 93dB with 4 watts, 96dB with 8 watts, 99dB with 16 watts, 102dB with 32 watts, and finally 105dB at 64 watts, right? So if I wanted a power amp to have a doubling headroom, I’d be looking for an amp with at least 124 watts/ch. Is this correct?

If I am understanding that correctly, then things get weird with, for example, a 90dB sensitivity speaker. -12dB at 4m = 78dB. This builds up to 512 watts needed for the same 105dB volume, and suggesting a power amp of minimum 1024 watts/ch. to give doubling headroom.

Sorry for this long question and likely bad math/understanding; I’m new to this hobby.