We can measure amplitude. Determine what is "loudness" is a perceptual thing. With our hearing being highly non-linear in this regard, the matching is non-trivial. The matching using noise is an approximation, not perfect matching.
Here are a few methods used for level matching in research papers:
Modeling Perceptual Characteristics of
Loudspeaker Reproduction in a Stereo Setup
CHRISTER P. VOLK,1,2 AES Student Member
(
[email protected])
, SØREN BECH,2,3 AES Fellow, TORBEN H. PEDERSEN1,
AND FLEMMING CHRISTENSEN2
View attachment 145339
Characterizing the Amplitude Response of
Loudspeaker Systems
Allan Devantier
Harman International Industries Inc., Northridge, CA, 91329, USA
View attachment 145340
The Correlation Between Distortion Audibility and Listener Preference in Headphones
Steve Temme1, Sean E. Olive2, Steve Tatarunis3, Todd Welti4, and Elisabeth McMullin5
View attachment 145341