Here's a theoretical question that hopefully someone will be able to shed some light on. Apologies if this is the wrong forum, I figured the electrical engineering community would be more into loudspeakers but they probably don't understand acoustic resonance as well as the physics community.
I want to design an unconventional loudspeaker that can provide extremely high SPL in a small size low-voltage battery powered application.
- Available gain from amplifier: about 7 Vrms
- Desired power level: around 40W continuous
- Desired SPL: around 105dB @ 1metre (table saw, sporting event)
- Max diameter of loudspeaker: about 4cm. Depth unlimited.
Given the voltage and power requirements, Ohm's law dictates a very low speaker impedance of around 1.2 Ohms.
There are amplifier IC's that can provide enough current for such a low impedance at this power level. That part of the problem is solved. The remaining problem is to build a speaker that presents such a low impedance while maintaining (roughly) full-range output in a small size.
Flat frequency response is not a concern. I don't mind if the speaker has a bumpy frequency profile. But it should have somewhat usable low frequencies.
I understand that such speakers aren't really available off the shelf (correct me if wrong), so I'm thinking about unconventional designs. A couple of approaches that I think might work are making use of horns and acoustic resonance.
Would a tiny speaker attached to a long hollow horn-like structure, that flares at the end and contains chambers for acoustic resonance along it's length, be able to achieve these specs? (Horn length is not a constraint)
What are the relevant equations for relating the acoustic properties of a loudspeaker to the electrical impedance presented by the loudspeaker's transducer?
How can I most efficiently convert electrical power flowing through a tiny transducer into acoustical energy, using unconventional means without caring about a flat frequency response?
Any ideas or suggestions towards solving this problem would be greatly appreciated :)
Any solution that addresses the key main points of 1. very high SPL 2. small cross sectional area and 3. low voltage/impedance will be considered the correct answer.