Why is the reference pressure for dB SPL 20uPa?

Question

The article here says that

This 20-micropascal reference was selected because it was the quietest sound pressure level that a group of normal hearing test subjects could detect.

which makes me think it should be the smallest sound that a normal human ear should be able to detect.

However, if we look at the db HL scale of an audiogram (0 dbHL = smallest audible sound at a given frequency for an ear with normal hearing), and a typical dBHL to dBSPL conversion table as given here, 0 dBHL at non of the frequencies are even close to 0 dBSPL. The smallest dBSPL value that is 0 dBHL is at 1000 Hz, and it is 7.5 dBSPL, which turns out to be 47.43uPa, much larger than the reference 20uPa. I expected 0 dBHL for at least some frequencies to be close to 0dBSPL but that's not the case.

What is the logic behind using 20uPa as the reference for the dBSPL? Is it actually the smallest sound an ear can hear, or is there something else?

Answer 1

It's complicated.

Let's take it step by step:

1. Sound pressure is a physical quantity that's related to the intensity of the sound field where you measure the pressure. It's measured in Pascal $Pa = \frac{N}{m^2}$ (an actual pressure).
2. Since audible sound covers a huge dynamic range, we often use a logarithmic scale. This needs a reference which happens to be $p_{ref} = 20 \mu Pa$. The choice of reference is one of convenience. It doesn't much matter what exactly it is, as long as it's used consistently. This one happens to make the vast majority of real world measurements fall in the range between 0dB SPL and maybe 140 dB SPL. These are just "nice numbers" to work with.
3. Perceived loudness is perceptual quantity, not a physical one. It's certainly related to physical sound intensity but the relationship is very very complex. A signal that measures 50dBSPL can be substantially louder than a signal that measures 70dBSPL
4. Perceived loudness varies A LOT with frequency and with overall level. For sine waves this has been intensively studied and the "official" version has been standardized in ISO 226 (https://www.iso.org/standard/34222.html) . These are in the form of equal loudness curves/contours (ELC) referenced to a sine wave at 1 kHz.
5. A crude attempt to estimate perceived loudness for complex signals are "weighting" curves which attenuate or boost certain frequencies based on the ELC before calculating the power or energy https://en.wikipedia.org/wiki/A-weighting. A-weighting is based on the ELC for moderate sound levels and C-weighting is based the ELC at high levels
6. db HL is another type of weighting curve specified in Ansi S3.6 (https://webstore.ansi.org/Standards/ASA/ansis31996). It's specifically targeted at audiometers, i.e. devices to measure hearing loss.

The original choice of $p_{ref} = 20 \mu Pa$ is based on early measurements that put the threshold of hearing for healthy humans for a 1kHz sine wave roughly at $20 \mu Pa$. These type of measurements are notoriously difficult to make and it's not unusual to find more than 10dB+ differences in the literature. At some point you just need to pick one.

I haven't read the ANSI standard for dB HL (since it's behind a paywall) but I'm guessing, it's based on clinical considerations and practicalities of audiometers in the field, which tend to have a high margin of error. From the looks of it, it appears to be influenced a lot of what a medical professional would consider a problem. For example according to ISO 226, the threshold of hearing at 125 Hz is about 17 dBSPL. That corresponds to a whopping -28 dB HL. In other words, Ansi S3.6 doesn't consider hearing loss at 125 Hz a problem unless it exceeds 28 dB. This may be related to the fact that 125Hz contributes very little to speech intelligibility but that's just a wild guess.

Answer 2

First, it's 20uPa, not 2uPa as you wrote several times.

When you ask ten people to measure the hearing threshold across frequency, you will get ten different answers, as it strongly depends on

• method,
• equipment
• and, most strongly, the test group.

That's what happened here. At one point in time, someone did some measurements on some people and determined the absolute threshold of human hearing to be 20uPa at 1000Hz. Then, at some other point in time, someone else did essentially the same thing, but his find was somewhat different from the first guy's. Nothing to ponder here, competing standards are quite normal, especially if the investigated object is a person. The good news is, the standard curve of hearing threshold in dBSPL is not that different from the conversion table you gave.