Two sources on the same tone have the same fundamental, so the same pitch. What differs is the timbre: which overtones sound strongly along and which hardly. Overtones are whole multiples of the fundamental that sound at the same time, and together they form one wave. That mix sets the sound of its own.
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I sing two vowels at exactly the same pitch and equally loud, and still you hear at once that they are two different things. Where does that difference sit? Not in the pitch, because that is the same.
You first see what the lowest tone of a vibrating string depends on: on the length, the thickness and the tension, and with an instrument you blow into on the length of the air column. That lowest tone is the fundamental. But a string does not vibrate only at its fundamental: it vibrates at the same time at whole multiples of it, and those are the overtones. With a fundamental of two hundred vibrations per second, four hundred, six hundred and eight hundred sound along as well, weaker than the fundamental. All those vibrations are added together into one wave, and that is why you hear only one tone. Which overtones sound strongly along and which hardly, that is the timbre, and that is where the difference sits.
Note for readers used to AQA: what we call the first overtone appears on an exam paper as the second harmonic.
For upper secondary physics, in the chapter on sound. Halfway there is a question and a silence: pause it there and think for yourself first.
In this video
The full explanation, in writing
The problem
0:01Same pitch. Equally loud. And still you hear at once that they are two different things.
What the lowest tone depends on
0:13Start at the beginning. Pluck a stretched string and it starts vibrating. The tone you hear belongs to the lowest frequency at which that string can vibrate, and that we call the fundamental. What that fundamental depends on you can see in three steps.
0:27Make the string shorter and the fundamental goes up. Take a thinner string and the fundamental goes up. Stretch it tighter and the fundamental goes up again. With an instrument you blow into, the same story sits in the air itself. There the length of the vibrating air column sets the fundamental: the longer the air column, the lower the tone.
0:53And that is why the tone changes when you open or close holes, because with that you make the air column shorter or longer. Here are two stretched strings. Equally long and equally thick, but the top one is stretched tighter. Which of the two gives the highest tone?
What else sounds along
1:15Now the part almost nobody expects. That string does not vibrate only at its fundamental. It vibrates at the same time at frequencies that are whole multiples of that fundamental, and those we call the overtones. Take a fundamental of two hundred vibrations per second.
1:33Then that same string vibrates at that same moment at four hundred too, and at six hundred, and at eight hundred. Two times, three times, four times the fundamental. Note the word at the same time. They are not tones that come one after the other, and they are not tones you hear separately.
1:50They are all there at the same moment. And they are weaker than the fundamental: the amplitudes of the overtones are smaller.
Why you hear only one
2:00If those four vibrations are there at once, why do you hear only one? Because they are added up. At every moment you add the displacements of the fundamental and of all the overtones together, and what you keep is one wave. One jagged wave, that looks very different from those neat separate waves.
2:22That is the complex tone. Your ear takes in that one wave. And so you hear one tone as well, with the pitch of the fundamental. The overtones you do not hear as separate tones. You hear them in the character of the sound.
The sound of its own
2:39And now back to the beginning. What then makes the difference between those two sounds just now? Not every overtone is amplified equally strongly. That depends on what the vibration has to go through: on the material, the shape, on the size of the space around it.
2:56Some overtones come out amplified, others hardly. Which overtones are strong and which weak, that sets the sound of its own. That we call the timbre. With "ah" and "oo" I change only the shape of my mouth. The vibration of my vocal cords does not change, so the fundamental stays exactly the same.
3:18But the shape of the space above it changes, and with it which overtones are amplified. Same fundamental, different mix, different sound.
An octave is not an overtone
3:30There is one more word you need, and it is often confused with an overtone. If you double the frequency of a musical tone, you get the same musical tone again, only higher. You then say that tone lies an octave higher. From two hundred to four hundred is therefore an octave.
3:50And there sits the confusion. Four hundred is also the first overtone of that fundamental of two hundred. Still they are two very different things. An octave is a distance between two tones that you play one after the other. An overtone sounds along inside the same tone, at the same moment, without you doing anything for it.
4:12Apart from each other, or at the same time. That is the difference. Three things to remember. One: the fundamental is the lowest tone of a vibrating string or air column, and it depends on the length, and with a string also on the thickness and the tension.
4:28Shorter, thinner, tighter: all three higher. Two: along with the fundamental the overtones sound, at whole multiples of the fundamental and with smaller amplitudes. Added up they form one complex tone. Three: which overtones become strong and which weak, that is the timbre.
4:50That is why the same tone on two sources does not sound the same. Two questions. First question: a fundamental is a hundred and fifty vibrations per second. What are the first two overtones? Second question: two sources both play exactly the same tone, equally loud, and still you hear the difference at once.
5:10What then does differ? The first: overtones are whole multiples, so two times a hundred and fifty is three hundred, and three times a hundred and fifty is four hundred and fifty. If you get three hundred and six hundred, you have doubled each time instead of adding the fundamental each time.
5:32And the second: the timbre. The fundamental is the same for both, because the pitch is the same. What differs is which overtones sound strongly along and which hardly. You now know what the fundamental depends on, that overtones sound along on top of it, and that the mix of those makes the sound of its own.
5:53How you work out the tone a tube of a given length gives, there is a separate video about that on the channel.
Frequently asked questions
What is the difference between an overtone and an octave?
An octave is a distance between two tones you play one after the other: a doubling of the frequency. An overtone sounds along inside the same tone, at the same moment, without you doing anything for it. Four hundred is both an octave above two hundred and its first overtone, and that is where the confusion comes from.
What are the first two overtones of a fundamental of 150 hertz?
Three hundred and four hundred and fifty. Overtones are whole multiples, so two times and three times the fundamental. If you get three hundred and six hundred you have doubled each time instead of adding the fundamental each time.
Why do you not hear overtones as separate tones?
Because at every moment their displacements are added to that of the fundamental, so your ear takes in one wave. You hear one tone, with the pitch of the fundamental, and you hear the overtones in the character of the sound.
What does the fundamental of a string depend on?
On the length, the thickness and the tension. Shorter, thinner and tighter all give a higher fundamental. With an instrument you blow into it is the length of the vibrating air column, which is why opening and closing holes changes the tone.
Why do two instruments playing the same note sound different?
Because not every overtone is amplified equally strongly. That depends on the material, the shape and the size of the space around the vibration. Which overtones come out strong and which hardly is the timbre.
Overtones you do not hear as separate tones. You hear them in the character of the sound.
Physics with Thomas makes physics explainers for secondary school. No words on screen, so what you see works in any language.
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.