Loudness is the way in which we perceive amplitude. As mentioned above, a particular change in amplitude is not necessarily perceived as being a proportionate change in loudness. That is because our perception of loudness is influenced by both the frequency and timbre of a sound. The 'just noticeable difference' or JND for amplitude, i.e. the minimal perceptible change in amplitude, varies by the starting amplitude and frequency, but in general ranges between 0.2 and 0.4 dB.
The most famous, well-used measurement for plotting our perception of loudness against the frequency of tones is the Fletcher-Munson curve(s) of equal loudness, published in 1933. The graphs were updated in 1956 by D.W. Robinson and R.S. Dadson. The purpose of the graph is to show that for humans to consider two pitches equally loud, the amount of energy necessary to produce the tone at one frequency may be completely different than at another. The multiple lines also show that the energy/frequency differences are steeper at lower intensity levels and flatten out at extremely high intensities.
The "loudness button" on a stereo amplifier is intended to boost bass frequencies at lower volume levels where the curve is the steepest. In viewing the graph, it immediately becomes apparent that much more acoustic energy is required in the lower frequencies to create sounds of equal loudness to those in higher frequencieswith a minimum around 4000 Hz, some additional energy is also required for equal loudness at higher frequencies. You do not buy a 500 watt amplifier for frequencies in the 5000 kHz range, but your might for equally loud bass in the 20-100 Hz range.
Most natural and instrumental sounds have the majority of their acoustic energy in the lower portion of their spectrathis naturally follows the way we hear. Certain synthesis methods, such as frequency modulation (FM) are prone to creating energy equally distributed across the spectrum, and so sound weighted toward the higher frequencies to us.
Above, there was mention of weighted methods of dB measurement that were more closely related to the way in which we hear. The most widely used is the A-weighted or dBA scale, which rolls off or progressively filters out lower frequencies and so creates a measurement in which all audible frequencies are treated equally for sounds of approximately 40 dB. This is a standard option on most dB meters and measurements should be indicated as dBA, not dB.
We had seen earlier that lower frequencies may mask higher frequencies on the basilar membrane, but the complete picture also involves amplitude. Masking occurs when the neurons of the basilar membrane fatigues and sensitivity to a particular frequency in the critical band of the neurons decreases. As a result a louder tone may mask a softer tone. The amplitude difference necessary to create masking depends on the frequency difference. The strongest masking response occurs with tones within the same critical band, where the least difference in intensity is required. It is also possible for sounds which are not simultaneous to exhibit masking, if the first tone is sufficiently loud and the subsequent tone occurs within a time span short enough for the neurons to stay fatigued. An extreme example of this might be how many bars of the 1812 Overture you miss following the cannon blast. Masking is yet one more psychoacoustic phenomenon a composer can take advantage of.