How can I calculate headphone driver excursion?

Question

I'm a headphone enthusiast, and once I tried to open up my headphones to see how much they move when I play my music.

However, I was really surprised to see that the sounds that I could "feel" actually came from a driver that didn't have any visible motion at all! The only way I could see even the smallest motions was by turning the volume up to extremely high levels that I would never listen to.

I tried to use the calculator I found here to calculate the motion that my headphones would make, and the results I got seemed to make sense, but this calculator was made for large speakers, not small headphones.

Could anyone tell me if this calculator should scale down to a headphone level (45 mm)? If not, what is an estimate for how much motion a headphone driver should be making at moderate volumes in terms of mm traveled?

Thank you!

Answer 1

I doubt that the calculator you referenced is relevant for headphones.

A fundamental difference between headphones and loudspeakers is that headphones transmit energy to the small, (almost) sealed, volume of air trapped between the headphone and the structure of your ear. That is completely different from a loudspeaker which is designed to transmit energy into a (theoretically) infinite region of air.

Since your ear responds to pressure variations in the air, for a small "sealed" volume of air the transducer movement to produce the same pressure change is roughly independent of the frequency - you are changing the volume of the trapped air by the same amount, and thus changing its pressure, independent of the frequency.

That is very different from a loudspeaker radiating into free air, where you need (approximately) the same velocity of the speaker cone to create the same pressure difference, and the displacement to produce that velocity is (approximately) inversely proportional to frequency - which is why high power bass speaker cones may move with an amplitude of several inches at low frequency, to produce the required sound pressure level.