>Why aren't speakers tested by measuring the output sound waves vs the input wave signals?
Because it's less relevant due to how our hearing works than other measurable parameters like intermodulation distortion and stored energy.
The phase distortion (reproduced via electronic all-pass filters so that the effects can be tested without the polar response differences that go with multiple drivers and varying cross-over functions) by cross overs through fourth order at typical frequencies is not detectable in blind comparisons with musical signals (clicks at long intervals can be differentiated).
While first order acoustic cross-overs avoid that they also allow excursion to double at a given input signal level for each octave below the cross-over point until their slope gets steeper. To avoid audible distortion as you reach the speakers' mechanical limits you need a higher cross-over point which means the lower frequency driver is becoming acoustically large with increasing directivity so there's a bigger directivity mismatch switching between drivers. You also have a +3dB peak off-axis someplace which isn't something our brains encounter in nature. I speculate that these reasons are why first order designs don't sound natural.
>Assuming you control all the other parameters of the test of course...
You'd do well to read _Sound Reproduction: Loudspeakers and Rooms_ by Floyd Toole. It does a great job summarizing what we know about hearing and sound reproduction.
Because it's less relevant due to how our hearing works than other measurable parameters like intermodulation distortion and stored energy.
The phase distortion (reproduced via electronic all-pass filters so that the effects can be tested without the polar response differences that go with multiple drivers and varying cross-over functions) by cross overs through fourth order at typical frequencies is not detectable in blind comparisons with musical signals (clicks at long intervals can be differentiated).
While first order acoustic cross-overs avoid that they also allow excursion to double at a given input signal level for each octave below the cross-over point until their slope gets steeper. To avoid audible distortion as you reach the speakers' mechanical limits you need a higher cross-over point which means the lower frequency driver is becoming acoustically large with increasing directivity so there's a bigger directivity mismatch switching between drivers. You also have a +3dB peak off-axis someplace which isn't something our brains encounter in nature. I speculate that these reasons are why first order designs don't sound natural.
>Assuming you control all the other parameters of the test of course...
You'd do well to read _Sound Reproduction: Loudspeakers and Rooms_ by Floyd Toole. It does a great job summarizing what we know about hearing and sound reproduction.