Energy in noise canceling headphones
For a long time, noise canceling headphones have intrigued me. I do understand the principle of calculating a sound wave to interfere destructively with the noise. It just feels astonishing to me that it can be done quickly enough in such a small space. A great feat of engineering!
Anyway, I just started to wonder about the energy. The original noise carries energy, and so does the canceling wave. Outside the target area they do whatever, but inside it the waves cancel each other (not perfectly, but still). What is left supposedly carries less energy. So where does the rest go?
My guess goes to the usual suspect: the energy is converted to a bit of heat and quickly dissipates to the surrounding air and flesh and plastic and whatever is there. Is this right? And as a funny additional question: how loud would the noise have to be for the headphone wearer to feel this heat?
1 reply
This is a really good question, I couldn't find an explanation online that dumbs it down enough for my high-school physics knowledge.
My initial uneducated guess was that the headphone speaker spends energy to shape the waveform back to flat. As in the background sound comes in as different air pressures, and the headphone speaker uses energy to constantly move against the wave. Like how two object colliding in opposite directions can result in no motion after impact, the energy goes into changing the course of the motion.
But the few people answering the general question of destructive interference and conservation of energy, they often say that any interference will be both destructive and constructive in different locations. Overall the system as a whole will still have the same amount of energy when averaged out.
It's a really interesting example of classical physics that's still quite unintuitive, at least to me. I've only experienced sound wave interference by playing a low frequency sound wave around 100Hz on a speaker in a large room. Walking around, you can hear the tone get louder and quieter in different places, on the scale of it's wavelength that's around 3.5 metres. I can't fully grasp how destructive interference happens in the tiny gap between the headphone and the ear, it's much smaller than most of the wavelengths you are hearing.