MELISSA BLOCK, HOST:
And now a vexing problem solved.
HENRIQUE OLIVEIRA: Tick-tock, tick-tock.
BLOCK: This is mathematician Henrique Oliveira. And for a while, he's tried to solve a problem that scientists have pondered for 350 years.
AUDIE CORNISH, HOST:
If you put two pendulum clocks next to each other on a wall, eventually they'll sync up.
BLOCK: As one pendulum swings to the left...
CORNISH: The other swings to the right.
OLIVEIRA: They swing in opposite directions forever (laughter). It's amazing. It's mesmerizing.
BLOCK: The question is why?
CORNISH: In a new study published in the journal Scientific Reports, Oliveira offered the answer.
BLOCK: Which is essentially sound waves - insistent little pulses that travel from one pendulum to the other.
OLIVEIRA: They swing as they were talking one to each other, so each one of the clocks is going to perturb the second one.
BLOCK: And yes, the word is perturb.
OLIVEIRA: Perturb, exactly, the exact term is perturbation.
BLOCK: Perturbation is what happens when sound pulses move through a beam on the wall that holds the two clocks. Each sound pulse is like a little kick, and those kicks add up.
OLIVEIRA: They listen to each other. They listen to the ticks and the tocks of each other and that adjusts each one to a proper antiphase swing.
BLOCK: That's phase opposition, and when the clocks reach that state, one pendulum swings right...
BLOCK: As the other swings left.
CORNISH: They stay that way.
OLIVEIRA: Tick-tock.
CORNISH: Mesmerizing.
OLIVEIRA: Tick-tock, tick-tock.
CORNISH: Henrique Oliveira, a mathematician at the University of Lisbon and co-author of the study that appeared this month in the journal Scientific Reports. Transcript provided by NPR, Copyright NPR.