Sound and Waves

An old engraving shows a large horn lying on its side, connected to a cylinder turned by a crank. — Édouard-Léon Scott de Martinville’s phonautograph, 1859 model: engraving published in 1865 in a book by Franz Josef Pisko. Édouard-Léon Scott de Martinville (1817–1879), Public domain, source

The same noise can measure 150 dB in water and 90 dB in air. Yet it is exactly the same energy.

This page is about decibels, and it is the best place on the site to address a fundamental question: what exactly does this number count?

1. First, what a sound is

A sound is matter that vibrates.

When you strike a drum, the skin trembles, pushes the air touching it, that air pushes the neighbouring air, and so on all the way to the ear. Sound travels through a succession of compressions and expansions in a medium — air, water, metal.¹

No matter, no sound. In space, nothing can vibrate: an exploding spaceship makes no noise there. It is one of the few errors of physics that most science-fiction films still perpetuate.

The stiffer the medium — the harder it is to compress — the faster sound travels. (It is not density that counts: at equal stiffness, a denser medium slows sound down. Steel is fast because it is very stiff, despite its weight.)²

Medium	Average speed	Practical example
Air	~ 340 m/s	Standard propagation in everyday life
Water	~ 1,500 m/s	Underwater sounds and echolocation
Steel	~ 6,000 m/s	You hear the train on the rail before you hear it through the air

Sources for the table³

2. What makes a sound high or low

A guitar string that vibrates fast produces a high sound. The same string, slacker, vibrates slowly and produces a low sound. What changes is the number of back-and-forth movements per second: the frequency.

It is measured in hertz: one hertz corresponds to one vibration per second. The low E string of a guitar vibrates about 82 times per second; the high E string, about 330 times. That is four times faster, two octaves higher.⁴

The human ear perceives roughly 20 to 20,000 hertz. This is a range, not a boundary: it narrows with age, especially at the top, and a fifty-year-old adult rarely hears above 15,000 hertz. What you hear at a given age, you will not hear all your life.⁵

Beyond these limits, sound still exists — it is the ear that stops, not physics. Below 20 hertz, we speak of infrasound: elephants use it to communicate over several kilometres. Above 20,000 hertz, of ultrasound: bats use it to see in the dark.

Two different notions must not be confused. Frequency distinguishes high from low. The decibel, which the whole rest of this page deals with, distinguishes loud from soft. A very high sound can be very soft, and a very low sound can be deafening. These are two independent scales.

3. The decibel is not a unit

A metre is a metre. A kilogram is a kilogram. These are units: they measure an absolute quantity.

The decibel is not a unit. It is a ratio.⁶

It does not directly measure a quantity of sound: it compares the energy of a sound with a chosen reference. Reading “60 decibels” means “60 decibels above the reference”. In air, this reference is a fixed convention close to the faintest sound a normal human ear can perceive (20 µPa).⁷

Without the reference, the number loses all meaning.

The evidence from water

Underwater, acousticians use a different reference (1 µPa), twenty times smaller. The result: a sound of the same physical energy is measured at about 61 decibels more in water than in air.⁸

150 dB underwater ≠ 150 dB in air.
A single number, two distinct conventions, two different physical realities.

But the quick explanation, the one found almost everywhere, calls for caution: “the gap comes from the change of reference”. This is true, but insufficient.

Going from 20 to 1 micropascal amounts to dividing the reference by twenty — which produces only 26 decibels of difference. Thirty-five are therefore missing.⁹

They come from elsewhere: water resists the passage of a wave far more than air does. Acousticians call this impedance. At identical pressure, a wave carries much less energy in water than in air, and this second effect is worth about 35.5 decibels.¹⁰

What produces the gap	How much
The change of reference (20 → 1 µPa)	~26 dB
The difference in impedance between water and air	~35.5 dB
Total	~61.5 dB

Sources for the table¹¹

The method matters more than the numbers. An explanation that accounts for the right result is not necessarily the right explanation: here, the reference alone gave 26 instead of 61. When correct reasoning does not add up, something is missing from it.

One warning remains, from the specialists themselves.

This figure of 61.5 circulates widely, and acousticians are wary of it. They write that it is inappropriate to suggest that subtracting 61.5 decibels “converts” an underwater level to its airborne equivalent.¹²

The reason: the conversion settles the question of physics, not that of perception. Hearing underwater and hearing in air are not alike; and comparing what a human hears with what a seal hears raises a problem that this calculation does not solve.¹³

These researchers say so plainly: it is better to apply this factor than to apply none — that has led to misleading comparisons — but its existence could confer a false sense of security. One believes one has compared; one has only converted.¹⁴

4. The scale does not advance evenly

On an ordinary graduated ruler, the distance between 10 and 20 is the same as between 20 and 30. The decibel scale, by contrast, is logarithmic: each step multiplies the value instead of adding to it.

+10 dB = 10 times more sound energy
+20 dB = 100 times more sound energy
+30 dB = 1,000 times more sound energy¹⁵

This is why a difference that looks small on paper can be enormous in reality. Between 85 and 115 decibels, the gap is only thirty points on paper; yet the second level carries a thousand times more energy.

5. A ratio is not a unit, and it is official

This is not a subtlety of wording: it is a matter of official nomenclature.

The International System of Units — the one that defines the metre, the kilogram and the second — does not count the decibel among its units. It classes it among the non-SI units, which serve to express logarithmic quantities.¹⁶

The reason is precisely the one given in the previous sections. A unit measures a quantity that exists independently of the observer: a metre remains a metre, whether one is measuring a table or a planet. A decibel, by contrast, says nothing until one has specified relative to what.

Many everyday numbers work this way without saying so. A percentage is a ratio. A stock market index is a ratio. An earthquake magnitude is a ratio. All are read as quantities, and none of them is one.

6. So what does this number count?

Back to the opening sentence: the same noise measures 150 dB in water and 90 dB in air.

Neither of the two numbers is wrong. Neither is rounded or approximate. Both are exact, and they describe the same physical event. What changes is the measurement convention — and a convention is neither true nor false; it is chosen.

From this follows a simple rule, which applies well beyond sound:

Before comparing two numbers, you must check that they count the same thing.

Two measurements in decibels can be compared only if they share the same reference. It is the same precaution as for the thresholds that define a city, the starting years that define a change, or the boundaries that define a fish stock. The number is solid; it is the sentence written above it that decides what it means.¹⁷

Note 1

The physical phenomenon of sound is defined to be a disturbance of matter that is transmitted from its source outward. […] These compressions (high pressure regions) and rarefactions (low pressure regions) move out as longitudinal pressure waves having the same frequency as the string—they are the disturbance that is a sound wave.

Urone, Paul Peter and Hinrichs, Roger, College Physics 2e, OpenStax (Rice University), 2022, section 17.1 “Sound”