Recently I was reading a book of acoustics and I came across the term “loudness”. Perhaps, because this term incorporates the word loud, hence “loud “+ “-ness” [1], it seems that i's quite easy to understand. My first thought  was that "Loudness is a term that is used to characterize how loud a sound is. The louder the sound, the highest its loudness".

However, the aforementioned definition lacks clarity. I have used words like "loud" and "high", but not even these two words are simplifing anything. For instance, imagine you are sitting comfortably on your couch and you are listening a very peaceful peace of music, e.g. a romantic song on a piano, perhaps a guitar etc. Suddently, a car with a very noisy engine passes by your house and your tranquility is suddently ruined. Fortunately, this lasts only a few seconds. At that momment the peaceful music you were listening comes back. However somethig weard happens. Your music appears to be less loud than before. How is that possible? You didn't lower the volume of your stereo system, nor you have moved away from your couch.

Today, I will try to demistify this term. Unfortunately, although I have found in the literature quite a lot of definitions, most of them contain jargon, which is however necessary for its better understanding. For this reason, I will try to simplify the terminology, but if it's necessary I will use the approprate scientific term. 

Before I give a formal definition for loudness, it's better to investigate a little bit more the figures on the side. The first picture (fig. 1) indicates roughly how loud a sound is based on everyday experiences. For instance a normal conversation is 60 dB (decibels), while a rock concert at around 110 dB. At 140 dB is the so called "threshold of pain" at which a pain begins to be felt and a long exposure of sounds of that amplitude can cause damage to human hearing. Finally at 0 dB is the "threshold of hearing" at which a sound becomes just audible. Most of the times dB is refered as dB SPL (Sound Pressure Level), to indicate the physical amplitude of a sound.

Nevertheless, a sound is not the same loud at all frequencies. Let's try to understand the 2nd figure (fig. 2). Firstly, the figure indicates that the range of hearing is between about 20Hz (like a bass) and 20kHz (like a soprano), and we are most sensitive at frequencies between 2kHz and 4kHz which is important for speech. The light green area is the "auditory response area"  because we can hear tones that fall within this area. The dark green area is where mainly the the conversational speech resides. At the borders there is the "threshold of hearing" and the "threshold of of pain".

A nice definition I found and I realy liked was that of  Moore [2],

Loudness is the perceptual correlate of the intensity of the acoustic stimulus. Because loudness is subjective, it is very difficult to measure in a quantitative way. Estimates of loudness can be strongly affected by bias and context effects of various kinds. For example, a sound with a moderate level (say 60 dB SPL) may appear quieter when presented just after a highlevel sound (say 100 dB SPL) than when presented before the high-level sound.

Imagine now that that you have somebody talking to you at 40 dB SPL (point C). If you had at the same sound level a sound at 30Hz (point A) then this sound wouldn't be audible, while if it was at 50Hz (point B) then it would be. The red line (point C) indicated as 40 phon is the level that is necesseary to have for other frequencies in order to create the same perception of loudness [3]. The curves in fig. 2 are called equal loudness curves [4]. For instance a sound with high frequency, e.g. a soprano or a piccolo at around 10kHz, in order to produce the same perception of loudness as a middle range sound, e.g. a tenor or a violoncello at around 1kHz,  has to have higher amplitude, or differenly expressed in order these sounds to have the same perception of loudness at 60 phons, the 10kHz has to be around 70 dB SPL, while the sound of 1kHz has to be at 60 dB SPL [3]. Weird...isn't it?

If you are playing music at a fairly high level, e.g. at 80 dB SPL, you would be able to hear all frequencies between 20 Hz and 5kHz (80 phons curve). However, if you turn the level down to 10 dB SPL, all frequencies don’t sound equally loud. Below 400 Hz (the bass notes) and above about 12kHz (the treble notes) are inaudible at 10 dB. Being unable to hear very low and very high frequencies at low dB levels means that when you play music softly you won’t hear the very low or very high frequencies. To compensate for this, some stereo receivers have a button labeled “loudness” which boosts the level of very high and very low frequencies when the volume control is turned down. This enables you to hear these frequencies even when the music is soft [3].

After all this explanation, we haven't answered how it's possible to have this feeling of our music sounding less loud when a track is passing by. For that, let's observe fig. 3 [5]. We can notice the 40 phon equal-loudness contour and a bar that indicates a noise, e.g. a noisy engine, called masker. When the masker is present the contour changes and around the frequencies of the masker the sound level is increased. This means in order for us to be able to listen a sound, e.g. our music, around that level we need to increase the volume of our stereo system. Does it sound familiar?

Now can you understand why when a noisy car (masker) passes by your house the music afterwards sounds lower? It's simple...As we mentioned in our definion and we notice in fig. 3 the loudness can be affected by various conditions [2]. When a car is passing by the loudness contour that corresponds to the music we listen changes, in fact it increases around the frequency content of the noisy car. When the car is getting away the equal-loudness contour is getting back again to the former state, which corresponds to a decrease on the loudness. Amazing?

So I hope, the next time a car ruins your quietness, you will know how it might affect your perception to the music you listen.