Read transcript
You know the sound. It's late, the light is off, you're nearly asleep, and a thin whine drifts past your ear. You don't need to see it. You already know it's a mosquito and not a bee, because a mosquito is high and sharp, and a bee is lower and rounder.
But a mosquito has no throat. Neither does a bee. So where is the note coming from, and why are the two notes different?
If you once scored zero in physics, stay with me. The answer is a kind of counting, and you've been counting since you were small enough to use your fingers.
The idea: count, then divide
Plenty of things around you repeat. A second hand ticks. Your heart beats. A swing goes out and comes back. Some things repeat too fast to see: a plucked guitar string is just a blur, and the string keeps going back and forth while you hear one steady note.
To describe anything that repeats, "fast" and "slow" aren't enough. You need two numbers: how many times it happened, and how long you watched. Then you divide:
is the frequency, is the number of repeats, and is the time. The unit is "times per second", which has a name, the hertz (Hz).
This formula didn't fall from the sky. It grew out of the first formula in my series, speed, : how far, divided by how long. Keep the bottom the same, time. Swap the top from distance to a count . Speed asks how far you went in each second. Frequency asks how many times something happened in each second. On my formula tree, frequency is a branch that grew straight out of speed.
You don't have to count for exactly one second, either. A doctor taking your pulse often counts for 15 seconds. Say she gets 18 beats:
Times 60, that's 72 beats a minute.
Now turn the question around. If something happens times each second, how long does one time take? Think of one second as a cake. Cut it into equal slices, and each slice is of a second. That slice is the period:
Frequency asks "how many times in a second?" Period asks "how many seconds for one time?" Same fact, seen from two sides.
Back to the bedroom. A female mosquito, the one that bites, beats her wings roughly five or six hundred times a second. Call it 500. Each beat then takes , two thousandths of a second. A honeybee hovering beats about 230 times a second. The wings push the air, the air carries the push to your ear, and your ear hears fast repeats as pitch. More beats per second means a higher note. That's the whole mystery. The mosquito is high because she's fast.
The people who built it
Writing takes one line. It took people more than two thousand years to get there.
Tradition says Pythagoras, in ancient Greece, found that half a string sounds an octave higher, and two thirds of it sounds a fifth higher. He left no writings, so we say "tradition says". The famous story of him hearing it in a blacksmith's hammers turns up about six hundred years after his death, and it doesn't work physically.
In the Warring States period, the book called the Guanzi, compiled by scholars long after the statesman whose name it carries, worked out the five notes by repeatedly taking a third away or adding a third. Taking away a third is the same 3:2 ratio. Two ends of the world, the same number. In the state of Zeng, craftsmen cast the bells buried with Marquis Yi of Zeng around 433 BCE. Each bell gives two different notes depending on where you strike it. Much later, in 1584, Zhu Zaiyu, a prince of the Ming dynasty who preferred mathematics to his title, became one of the first people to calculate equal temperament precisely: the twelve equal steps a piano uses today.
But all of these people were measuring lengths. Nobody yet knew what the lengths stood for.
In Florence, in the Grand Duchy of Tuscany, a lute player named Vincenzo Galilei decided to test what the old books said. Around 1589 he found that to raise a string by an octave you need four times the weight hanging on it, not twice. His son Galileo studied the pendulum. A popular story says he timed a swinging lamp in Pisa cathedral against his own pulse, though that story comes from a student writing years later. What we know for sure is a letter Galileo wrote in 1602 about pendulum experiments. A swing takes nearly the same time whether it's big or small. Something that repeats in equal times can measure time.
Strings vibrate far too fast to count by eye. In 1636, in the Kingdom of France, Marin Mersenne got around this in a stubborn way. He used a very long, very slack string, over twenty metres, so slow he could count its swings, then worked out what shorter strings would do. For the first time, someone put a number of vibrations per second on a note you could hear. Two years later, Galileo noticed that scraping a brass plate with a chisel sometimes made it squeal and left even little ridges behind. A higher squeal left more ridges.
Then, in England, on 8 August 1666, Samuel Pepys wrote in his diary that Robert Hooke had told him something odd: if you knew how many vibrations made each note, you could listen to a fly and say how many times a second it beat its wings. Pepys thought this a little too much. But Hooke meant it. In 1681, at the Royal Society in London, he spun a toothed brass wheel against a striker. Each tooth made a click, and fast clicks blurred into a note. Count the teeth, count the turns, and you know the frequency. A wheel with 100 teeth turning five times a second sings at 500 hertz. That's our mosquito.
The unit came last. In the 1880s, in Karlsruhe, in the Grand Duchy of Baden within the German Empire, Heinrich Hertz made and caught electromagnetic waves. He died at 36. In the 1930s, the International Electrotechnical Commission named the unit after him, and in 1960 the hertz entered the International System of Units. He never used the word himself.
Where you meet it
Your quartz watch has a tiny crystal vibrating 32,768 times a second. That number is 2 to the 15th power, so the circuit halves it fifteen times and lands on exactly one tick a second.
The power in your wall goes back and forth 50 or 60 times a second, depending on where you live. In 1891 a German electrical company saw lights flicker at 40 hertz and moved up to 50.
Since 1967, the second itself has been defined by counting. One second is the time taken by 9,192,631,770 cycles of a particular microwave signal that caesium atoms respond to. Your phone's satellite navigation depends on clocks like that. A timing error of one millionth of a second puts you about 300 metres off.
And a typical computer chip today ticks about three billion times a second. One tick lasts about a third of a nanosecond. In that time, even light only travels about ten centimetres.
What I take from it
When I look at , I don't really see the answer. I see the line of people behind it. Someone guessed right, someone guessed wrong, someone hung weights on a string because he didn't trust a book, someone spun a wheel in front of a doubtful friend. Each one handed the problem on a little clearer than they found it. The division at the end is the easy part. The counting took centuries.
That's why I'd rather show you how a formula was found than ask you to memorise it. If you learn the answer, you have one fact. If you follow the process, you can usually rebuild the answer yourself.
Nothing in physics arrives alone. Every formula has a parent, and sooner or later it has children.
Mosquito wings, guitar strings, pendulums, quartz, caesium atoms: the universe was vibrating long before anyone was here to count. We are part of that universe too. So when a person sits in the dark, hears a whine, and asks "how fast?", I like to think it's the universe slowly getting a look at itself.
Next time a mosquito finds you at night, you can be annoyed and amazed at once. Five hundred beats a second. Two thousandths of a second for each one. Then go and find a swatter.
— Hercules
Counting a Mosquito's Wings
You know the sound. It's late, the light is off, you're nearly asleep, and a thin whine drifts past your ear. You don't need to see it. You already know it's a mosquito and not a bee, because a mosquito is high and sharp, and a bee is lower and rounder.
But a mosquito has no throat. Neither does a bee. So where is the note coming from, and why are the two notes different?
If you once scored zero in physics, stay with me. The answer is a kind of counting, and you've been counting since you were small enough to use your fingers.
The idea: count, then divide
Plenty of things around you repeat. A second hand ticks. Your heart beats. A swing goes out and comes back. Some things repeat too fast to see: a plucked guitar string is just a blur, and the string keeps going back and forth while you hear one steady note.
To describe anything that repeats, "fast" and "slow" aren't enough. You need two numbers: how many times it happened, and how long you watched. Then you divide:
is the frequency, is the number of repeats, and is the time. The unit is "times per second", which has a name, the hertz (Hz).
This formula didn't fall from the sky. It grew out of the first formula in my series, speed, : how far, divided by how long. Keep the bottom the same, time. Swap the top from distance to a count . Speed asks how far you went in each second. Frequency asks how many times something happened in each second. On my formula tree, frequency is a branch that grew straight out of speed.
You don't have to count for exactly one second, either. A doctor taking your pulse often counts for 15 seconds. Say she gets 18 beats:
Times 60, that's 72 beats a minute.
Now turn the question around. If something happens times each second, how long does one time take? Think of one second as a cake. Cut it into equal slices, and each slice is of a second. That slice is the period:
Frequency asks "how many times in a second?" Period asks "how many seconds for one time?" Same fact, seen from two sides.
Back to the bedroom. A female mosquito, the one that bites, beats her wings roughly five or six hundred times a second. Call it 500. Each beat then takes , two thousandths of a second. A honeybee hovering beats about 230 times a second. The wings push the air, the air carries the push to your ear, and your ear hears fast repeats as pitch. More beats per second means a higher note. That's the whole mystery. The mosquito is high because she's fast.
The people who built it
Writing takes one line. It took people more than two thousand years to get there.
Tradition says Pythagoras, in ancient Greece, found that half a string sounds an octave higher, and two thirds of it sounds a fifth higher. He left no writings, so we say "tradition says". The famous story of him hearing it in a blacksmith's hammers turns up about six hundred years after his death, and it doesn't work physically.
In the Warring States period, the book called the Guanzi, compiled by scholars long after the statesman whose name it carries, worked out the five notes by repeatedly taking a third away or adding a third. Taking away a third is the same 3:2 ratio. Two ends of the world, the same number. In the state of Zeng, craftsmen cast the bells buried with Marquis Yi of Zeng around 433 BCE. Each bell gives two different notes depending on where you strike it. Much later, in 1584, Zhu Zaiyu, a prince of the Ming dynasty who preferred mathematics to his title, became one of the first people to calculate equal temperament precisely: the twelve equal steps a piano uses today.
But all of these people were measuring lengths. Nobody yet knew what the lengths stood for.
In Florence, in the Grand Duchy of Tuscany, a lute player named Vincenzo Galilei decided to test what the old books said. Around 1589 he found that to raise a string by an octave you need four times the weight hanging on it, not twice. His son Galileo studied the pendulum. A popular story says he timed a swinging lamp in Pisa cathedral against his own pulse, though that story comes from a student writing years later. What we know for sure is a letter Galileo wrote in 1602 about pendulum experiments. A swing takes nearly the same time whether it's big or small. Something that repeats in equal times can measure time.
Strings vibrate far too fast to count by eye. In 1636, in the Kingdom of France, Marin Mersenne got around this in a stubborn way. He used a very long, very slack string, over twenty metres, so slow he could count its swings, then worked out what shorter strings would do. For the first time, someone put a number of vibrations per second on a note you could hear. Two years later, Galileo noticed that scraping a brass plate with a chisel sometimes made it squeal and left even little ridges behind. A higher squeal left more ridges.
Then, in England, on 8 August 1666, Samuel Pepys wrote in his diary that Robert Hooke had told him something odd: if you knew how many vibrations made each note, you could listen to a fly and say how many times a second it beat its wings. Pepys thought this a little too much. But Hooke meant it. In 1681, at the Royal Society in London, he spun a toothed brass wheel against a striker. Each tooth made a click, and fast clicks blurred into a note. Count the teeth, count the turns, and you know the frequency. A wheel with 100 teeth turning five times a second sings at 500 hertz. That's our mosquito.
The unit came last. In the 1880s, in Karlsruhe, in the Grand Duchy of Baden within the German Empire, Heinrich Hertz made and caught electromagnetic waves. He died at 36. In the 1930s, the International Electrotechnical Commission named the unit after him, and in 1960 the hertz entered the International System of Units. He never used the word himself.
Where you meet it
Your quartz watch has a tiny crystal vibrating 32,768 times a second. That number is 2 to the 15th power, so the circuit halves it fifteen times and lands on exactly one tick a second.
The power in your wall goes back and forth 50 or 60 times a second, depending on where you live. In 1891 a German electrical company saw lights flicker at 40 hertz and moved up to 50.
Since 1967, the second itself has been defined by counting. One second is the time taken by 9,192,631,770 cycles of a particular microwave signal that caesium atoms respond to. Your phone's satellite navigation depends on clocks like that. A timing error of one millionth of a second puts you about 300 metres off.
And a typical computer chip today ticks about three billion times a second. One tick lasts about a third of a nanosecond. In that time, even light only travels about ten centimetres.
What I take from it
When I look at , I don't really see the answer. I see the line of people behind it. Someone guessed right, someone guessed wrong, someone hung weights on a string because he didn't trust a book, someone spun a wheel in front of a doubtful friend. Each one handed the problem on a little clearer than they found it. The division at the end is the easy part. The counting took centuries.
That's why I'd rather show you how a formula was found than ask you to memorise it. If you learn the answer, you have one fact. If you follow the process, you can usually rebuild the answer yourself.
Nothing in physics arrives alone. Every formula has a parent, and sooner or later it has children.
Mosquito wings, guitar strings, pendulums, quartz, caesium atoms: the universe was vibrating long before anyone was here to count. We are part of that universe too. So when a person sits in the dark, hears a whine, and asks "how fast?", I like to think it's the universe slowly getting a look at itself.
Next time a mosquito finds you at night, you can be annoyed and amazed at once. Five hundred beats a second. Two thousandths of a second for each one. Then go and find a swatter.
— Hercules