Why Is the Reference Pressure for SPL 20 μPa?
Sound pressure level, or SPL, is one of the most widely used decibel quantities in acoustics. It is defined as
where p is the RMS sound pressure and p0 is the reference sound pressure.
For airborne sound, the standard reference pressure is p0 = 20 μPa = 20 × 10 −6 Pa
This reference value is not arbitrary. It is related to both human hearing sensitivity and the physical reference intensity of sound in air.
Reference Pressure in Air
The value 20 μPa approximately corresponds to the threshold of human hearing at 1 kHz in air. In other words, it represents a very weak sound pressure that a young, healthy human ear can barely detect under ideal listening conditions.
When the measured RMS sound pressure is equal to this reference pressure, p = p0 = 20 μPa
the SPL becomes Lp = 20 log10 (20 μPa / 20 μPa) = 20 log10 (1) = 0 dB SPL
Therefore, 0 dB SPL does not mean absolute silence. It means that the RMS sound pressure is equal to 20 μPa, which is near the lower limit of human hearing in air.
Physical Meaning of 20 μPa
The reference pressure of 20 μPa is extremely small compared with atmospheric pressure.
Atmospheric pressure is approximately 101,325 Pa
The SPL reference pressure is 20 × 10−6 Pa
So the reference sound pressure is only a tiny fluctuation around atmospheric pressure. Sound is not the absolute air pressure itself, but a small dynamic pressure variation superimposed on atmospheric pressure.
This is why acoustic pressure is usually expressed in decibels rather than directly in pascals.
Relationship Between 20 μPa and Sound Intensity
The reference pressure of 20 μPa is also closely related to the reference sound intensity in air.
For a plane progressive wave, the sound intensity is approximately
where,
| Symbol | Meaning | Air | Underwater |
|---|
| I | sound intensity | I0 = p02 / ρc ≈ 10−12 W/m2 | I0 = p02 / ρc ≈ 6.7×10−19 W/m2 |
| prms | RMS sound pressure | p0 = 20 μPa | p0 = 1 μPa |
| ρ | density | 1.2 kg/m3 | 1000 kg/m3 |
| c | speed of sound | 343 m/s | 1500 m/s |
| ρc | characteristic acoustic impediance | ≈ 400 Pa⋅s/m | ≈ 1.5×106 Pa⋅s/m |
The airborne SPL reference pressure p0 = 20 μPa is approximately consistent with the commonly used reference sound intensity I0 = 10 −12 W/m 2 under plane-wave conditions.
The same pressure–intensity relationship applies in water, but the meaning of the reference is different. In air, 20 μPa is related to both human hearing threshold and the reference intensity 10− 12 W/m 2. In underwater, 1 μPa is mainly a standardized pressure reference; its corresponding intensity depends on the much larger acoustic impedance of water.
Difference Between Air and Underwater References
The difference between the two pressure references is 20 μPa / 1 μPa = 20
In decibels, this ratio corresponds to 20 log10 (20) ≈ 26 dB
Therefore, 20 μPa corresponds to 0 dB SPL in air, but relative to the underwater reference 1 μPa, the same pressure would be
20 log10 (20 μPa / 1 μPa) ≈ 26 dB re 1 μPa
This is why dB values in air and underwater acoustics cannot be compared directly unless the reference pressure and medium are clearly specified.
For example,
| Same RMS pressure | Level in air reference | Level in underwater reference |
|---|
| 20 μPa | 0 dB SPL | 26 dB re 1 μPa |
The number changes because the reference pressure changes.
Common Reference Pressures
The main reference pressures are
| Application | Reference pressure | Notation |
|---|
| Airborne sound | 20 μPa | dB SPL, dB re 20 μPa |
| Underwater sound | 1 μPa | dB re 1 μPa |
Thus, a complete dB expression should always include the reference. Saying only “100 dB” is incomplete because it does not specify whether the reference is 20 μPa, 1 μPa, or something else.
Conclusion
The reference pressure for airborne SPL is 20 μPa because it approximately corresponds to the threshold of human hearing at 1 kHz in air. It also corresponds closely to a reference sound intensity of 10−12 W/m2 under plane progressive wave conditions, through the relationship I = prms2 / ρc
In underwater acoustics, however, the standard reference pressure is 1 μPa, so underwater sound levels are expressed as
dB re 1 μPa not dB SPL. Because the reference pressure and the acoustic impedance of the medium are different, airborne and underwater sound levels cannot be directly compared by their dB numbers alone.
The essential rule is a sound level in dB is meaningful only when its reference pressure and medium are specified.
Suggested Further Reading
You may also find these topics helpful:
Why Is the Reference Pressure for SPL 20 μPa?
Sound pressure level, or SPL, is one of the most widely used decibel quantities in acoustics. It is defined as
where p is the RMS sound pressure and p0 is the reference sound pressure.
For airborne sound, the standard reference pressure is p0 = 20 μPa = 20 × 10 −6 Pa
This reference value is not arbitrary. It is related to both human hearing sensitivity and the physical reference intensity of sound in air.
Reference Pressure in Air
The value 20 μPa approximately corresponds to the threshold of human hearing at 1 kHz in air. In other words, it represents a very weak sound pressure that a young, healthy human ear can barely detect under ideal listening conditions.
When the measured RMS sound pressure is equal to this reference pressure, p = p0 = 20 μPa
the SPL becomes Lp = 20 log10 (20 μPa / 20 μPa) = 20 log10 (1) = 0 dB SPL
Therefore, 0 dB SPL does not mean absolute silence. It means that the RMS sound pressure is equal to 20 μPa, which is near the lower limit of human hearing in air.
Physical Meaning of 20 μPa
The reference pressure of 20 μPa is extremely small compared with atmospheric pressure.
Atmospheric pressure is approximately 101,325 Pa
The SPL reference pressure is 20 × 10−6 Pa
So the reference sound pressure is only a tiny fluctuation around atmospheric pressure. Sound is not the absolute air pressure itself, but a small dynamic pressure variation superimposed on atmospheric pressure.
This is why acoustic pressure is usually expressed in decibels rather than directly in pascals.
Relationship Between 20 μPa and Sound Intensity
The reference pressure of 20 μPa is also closely related to the reference sound intensity in air.
For a plane progressive wave, the sound intensity is approximately
where,
The airborne SPL reference pressure p0 = 20 μPa is approximately consistent with the commonly used reference sound intensity I0 = 10 −12 W/m 2 under plane-wave conditions.
The same pressure–intensity relationship applies in water, but the meaning of the reference is different. In air, 20 μPa is related to both human hearing threshold and the reference intensity 10− 12 W/m 2. In underwater, 1 μPa is mainly a standardized pressure reference; its corresponding intensity depends on the much larger acoustic impedance of water.
Difference Between Air and Underwater References
The difference between the two pressure references is 20 μPa / 1 μPa = 20
In decibels, this ratio corresponds to 20 log10 (20) ≈ 26 dB
Therefore, 20 μPa corresponds to 0 dB SPL in air, but relative to the underwater reference 1 μPa, the same pressure would be
20 log10 (20 μPa / 1 μPa) ≈ 26 dB re 1 μPa
This is why dB values in air and underwater acoustics cannot be compared directly unless the reference pressure and medium are clearly specified.
For example,
The number changes because the reference pressure changes.
Common Reference Pressures
The main reference pressures are
Thus, a complete dB expression should always include the reference. Saying only “100 dB” is incomplete because it does not specify whether the reference is 20 μPa, 1 μPa, or something else.
Conclusion
The reference pressure for airborne SPL is 20 μPa because it approximately corresponds to the threshold of human hearing at 1 kHz in air. It also corresponds closely to a reference sound intensity of 10−12 W/m2 under plane progressive wave conditions, through the relationship I = prms2 / ρc
In underwater acoustics, however, the standard reference pressure is 1 μPa, so underwater sound levels are expressed as
dB re 1 μPa not dB SPL. Because the reference pressure and the acoustic impedance of the medium are different, airborne and underwater sound levels cannot be directly compared by their dB numbers alone.
The essential rule is a sound level in dB is meaningful only when its reference pressure and medium are specified.
Suggested Further Reading
You may also find these topics helpful: