Decibels and Volume | Short Guide for Music Producers

What is volume | Frequency

Basically, the volume allows you to arrange the sounds from the quietest to the loudest. It’s a psychological feature. We can not measure it in physical units like Pascal, so db SPL; 0db = 20 μPa.

As well all know, the human ear begins to hear sound from a certain PS level.

(it is accepted that 0dB is 20 μPa).

But it turns out that along with the sound frequency, the threshold changes as well. What does that mean?

Based on the research conducted by Fletcher and Munson (published in 1993), lines of equal volume were determined. They show that the sound with a frequency of 4 kHz, with the sound pressure level of 94 db SPL (1 Pa) is not perceived as loud as the sound of 150 Hz with an identical sound pressure level of 94 db SPL (1 Pa).

Similar studies were carried our by many other researchers incl. Robinson and Dadson (1956), the results of which were adopted as the standard ISO 226 ( it is used now, with some modifications [ISO 226:2003])

Let’s look at the following chart:

From it, you can get a lot of useful information. How do we use it? Individual lines connect points with the same volume level. ( volume is feelings, so it’s psychoacoustics, not physics). For example, the line below represents the threshold of audibility. Based on studies conducted on a group of volunteers it was found out that so the man was able to hear a simple tone (sine wave) with a frequency of 1 kHz, the sound pressure level should be about 0dB. To hear a sound with a frequency of 300 kHz, you’ll need 10 dB. However to receive auditory sensations, caused by a tone with a frequency of 20 Hz, the sound pressure level has to be app. 80 dB (yes, 60 db, or even 70 dB will not be noticeable at all).

Human Ear behaviour

Turned out that the human ear can react to sounds depending on their frequency. So the phone unit was introduced.

Phones are represented by lines in the graph above (Equal-loudness contour). Equal-loudness contours show the exact pressure level in decibels, which, regardless of frequency will cause the listener to feel the impression of the same volume. So, phone is a unit of loudness.

So it would be easier for us to imagine how the frequency translates into pitch levels, let us listen through sine wave of 1 kHz, 4 kHz and 150 Hz.

To make sure that we understood the problem, let’s analyse the volume level of 50 phones (Equal-loudness contour passing through 1 kHz, 50 dB).

According to researches made by Robinson and Dadson (the graph is based on them). Hearing is most sensitive, when the frequency is 4000 Hz ( we are even able to hear negative decibels) and it’s least sensitive, when the frequency is 20 Hz.

If we wanted to listen to a 1 kHz sine wave with the level of 50 dB, and then we wanted to listen to a 4 kHz of the same volume, the level would have to be only 43 dB. On the other hand, if we wanted to hear a sine wave of the same volume level but with a frequency of 20 Hz, the level would have to be about 98 dB.

The human ear is that non-linear! That’s why we can’t really say that the SP levels and Volume levels are the same things.

To feel it on your own skin (or ear), let’s make a little experiment. We’ve got to make sure that the room that we’re using to listen to examples is completely silent.

Let’s follow the instructions from the video posted below.

Returning to the first chart, we can clearly see that the louder the sounds, the more linear is our hearing for lower frequencies.

The difference in volume, we have to make up to be able to hear the final repetition of the 100 Hz tone is 30 dB*.

It’s an interesting phenomenon of the Equal-loudness contour (0 phons) getting below 0 db.

SPL decibels are negative.

According to the observations of Fletcher and Munson, the human ear can hear negative decibels. Therefore a question arises, whether the 0 dB level is well selected. In my opinion No. If the Equal-loudness contour (0 phones) goes as low as -3 dB (about 14 μPa), this level is exactly what should define „0 dB”, not 20 μPa, like it does nowadays. But, that’s how it works, It got accepted because it’s easier to calculate (it’s easier to multiply 20 than to multiply 14)

In practice, adult humans are not able to hear such a level of sound pressure, so this should not pose any problem. But it’s good to be aware of this.

I hope I explained the problem and explained the hard relations between decibels and volume.

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*In practice it will be less that 30 dB, because at home, it’s rather difficult to eliminate background sound, sometimes it can even add +10 dB. In the conditions of anechoic chamber, that of course would be 30 dB.

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