Two tones with equal sound pressure can sound unequally loud. Blame your ears.
Loudness isn't just physics. Our ears are most sensitive between about 2,000 and 5,000 hertz, partly because of how the ear canal resonates, so deep bass and very high notes need much more energy to seem as loud. Mapping this took decades and threw up an unexplained scientific puzzle.
Human hearing spans roughly 20 to 20,000 hertz, with the upper limit falling as we age. But it is not equally sensitive across that range. We are most sensitive between about 2 and 5 kilohertz, largely because of the resonance of the ear canal and the way the tiny bones of the middle ear transmit sound. An equal-loudness contour is a curve showing how much sound pressure a pure tone needs at each frequency to seem as loud as a reference tone. Loudness measured this way has its own unit, the phon.
The first such curves were measured by Harvey Fletcher and Wilden Munson and published in 1933. Listeners heard pure tones through headphones and compared each with a 1,000-hertz reference, adjusted until the two seemed equally loud, and the results were averaged across many people. The lowest curve marks the quietest sound we can detect; the highest, the threshold of pain.
Then came the puzzle. A 1937 study disagreed with Fletcher and Munson over parts of the range, and in 1956 Robinson and Dadson produced new curves they believed more accurate, which became the international standard. But when a large international study coordinated from Tohoku University in Japan revised the standard as ISO 226 in 2003, it found that the 1956 curves were the odd ones out, differing by as much as 10 to 15 decibels at low frequencies, while the original 1933 curves agreed better. The reasons are still unexplained; suggestions include poorly calibrated equipment, different ways of judging loudness, and test subjects exposed to loud noise on the way to the lab.
The curves matter in everyday life. The A-weighting used in noise measurements was based on one of Fletcher and Munson's curves, and the ISO report called it fortunate that this curve matched modern results. Researchers later found that pure-tone curves do not fully describe how we perceive noise, which led to other weighting systems for audio equipment.
Source: Wikipedia — Equal-loudness contour · Text summarised from Wikipedia (CC BY-SA 4.0)
