At twice the distance, sound becomes four times quieter. A source spreads the same energy over a sphere that grows with the distance, and the area of that sphere grows with the square of the radius. Each halving is three decibels less, so twice as far is six decibels less.
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Stand twice as far from a speaker, and three quarters of the sound is gone. Not half: three quarters. And that is not because there is more air in between.
A sound source sends energy in all directions. Think of a sphere that grows around the source: everything the source emits is on that sphere, and the sphere gets bigger while nothing is added. At twice the distance the area of that sphere is four times as big, because an area grows with the distance squared. The same amount of sound over four times as much area: that is the inverse square law. Then you see how to go from times to decibels. Half as much sound is three decibels less, so standing twice as far is six decibels less. With a speaker in the schoolyard you work out what you measure at sixteen metres when it is a hundred decibels at two metres.
For upper secondary physics, in the chapter on sound. Halfway through there is a question and a silence: pause the video there and think for yourself first.
In this video
The full explanation, in writing
Two steps back
0:00Stand twice as far from a speaker, and three quarters of the sound is gone. Not half. Three quarters. And that is not because there is more air in between.
Where the sound goes
0:15A sound source sends energy in all directions. Think of a sphere that grows around that source: everything the source emits is on that sphere, and the sphere gets bigger while nothing is added. If you stand twice as far, the area of that sphere is four times as big.
0:34An area grows with the distance squared. The same amount of sound over four times as much area. Four times as little of it reaches your spot.
The inverse square law
0:46That is the inverse square law. Twice as far is two squared, so four times quieter. Three times as far, nine times quieter. Four times as far, sixteen times quieter. That holds in the open air. Inside a room it no longer works, because there the sound is also reflected back to you by the walls.
1:06Now you. You stand five times as far from the source. How many times quieter is the sound then?
From times to decibels
1:15Twenty-five times quieter. Five squared. Twice as much sound is three decibels more, so half as much is three decibels less. Standing twice as far is four times quieter, and that is halving twice: six decibels less. Twice as far is six decibels less.
1:35That is the number you need most often.
The speaker in the schoolyard
1:38There is a speaker in the schoolyard. At two metres you measure a hundred decibels. How much is it at sixteen metres? Sixteen divided by two is eight: eight times as far. Eight squared is sixty-four, so sixty-four times quieter. Sixty-four is six halvings.
1:56Six times three decibels less is eighteen decibels less. A hundred minus eighteen is eighty-two decibels. If you get ninety-one, you have skipped the square: eight times as far is not eight times quieter.
Summary
2:11Three things. One: sound gets quieter with distance because the same energy is spread over a larger area. Two: that area grows with the distance squared. Twice as far is four times quieter, three times as far is nine times quieter. Three: each halving is three decibels less, so twice as far is six decibels less.
The two questions
2:35Two questions. First question: you stand three metres from a sound source and you walk to twelve metres. How many times quieter is the sound there? Second question: and how many decibels come off then?
The answers
2:51Twelve divided by three is four times as far. Four squared is sixteen, so sixteen times quieter. Sixteen is four halvings, so four times three is twelve decibels less. You could also have done it per doubling: twice as far costs six decibels, and that twice is also twelve.
Wrap-up
3:12You can now work out how much quieter a sound gets when you move further away. On the channel there is a separate video about cancelling sound by adding sound.
Frequently asked questions
How many decibels do you lose when you stand twice as far away?
Six decibels. Twice as far is four times quieter, and four times quieter is halving twice. Each halving is three decibels less, so six in total.
A speaker gives 100 dB at 2 metres. How many dB is it at 16 metres?
82 dB. Sixteen divided by two is eight times as far. Eight squared is 64, so 64 times quieter, and 64 is six halvings. Six times three is eighteen decibels less, and 100 minus 18 is 82. If you get 91, you have skipped the square: eight times as far is not eight times quieter.
Why does sound get quieter the further away you are?
Because the same energy is spread over an ever larger area. The source sends sound in all directions, so it sits on a sphere that grows around the source. The area of that sphere grows with the square of the radius, so less and less of it arrives where you are. It is not because the air swallows the sound.
Does the inverse square law also hold in a room?
Not really. The inverse square law holds in the open air. In a room the sound is also reflected back to you by the walls, so it gets quieter more slowly than the law predicts.
Eight times as far is not eight times quieter. Do not forget the square.
Physics with Thomas makes physics explainers for secondary school. No words on screen, so what you see works in any language.
In this series
Sound and vibrationwhat you hear is not the air from his mouth6:53
Frequency, amplitude and pitchlouder is not higher5:57
Resonance and vibrating alongit is timing, not force6:17
Fundamental, overtones and timbresame tone, other sound6:06
The tone of an air columnf = v divided by 4L3:15
Decibels and loudness80 dB is not twice 40 dB3:31
Loudness and distancetwice as far, four times quieter3:27
Anti-noisemore sound and yet quieter2:31
The ear and hearing thresholdzero decibels is not silence5:38
Hearing damage and risk thresholdno pain does not mean safe6:23
About me
My name is Thomas Schuurmans, and I have a passion for physics and for understanding why things work the way they do. What I want is to get young people asking “why is that?” and “how does that work?” more often, and to hand them the tools of physics in a way that is simple and that you can see.
I graduated in applied physics at Delft University of Technology in 2003. After that I spent more than twenty years outside education: first at TNO, the Dutch applied research institute, then at a design agency, and eventually founding Proportion Global, through which I work on innovation questions in Africa, Latin America and South Asia. That work resembles physics more than you would expect: don't start from a solution, first understand what is going on, try something, be wrong, and look again.
Since 2026 I have been teaching physics to both lower and upper secondary classes, and I started a master's at the University of Amsterdam for my full teaching qualification. That is where I learned that a secondary school pupil's real attention for new material lasts about seven minutes. And my own weakness happens to be telling too many side stories.
That is where the idea came from: videos that explain one topic sharply and visually, inside those seven minutes. I make them for my own pupils. Then I publish them, because good explanation should be within reach of anyone who needs it, wherever you live and whatever language you think and speak in.