Sound enters the ear and hits a thin membrane inside the cochlea, the spiral organ in the inner ear. This membrane doesn't just vibrate like a string; it actively pushes the vibrations when they are weak and stops when they are strong. That's how the ear hears both a whisper and a loud conversation.
Scientists built a model where each piece of the membrane is a tiny pendulum with a spring. The spring pushes harder when vibrations are small and barely pushes when they are large. It's like a swing: if you give it a gentle push, it will swing higher, but if you push hard, you can't help it much more. This rule is called exponential.
The model also showed that the coupling between neighboring sections of the membrane is important. It widens the range of audible frequencies and changes the shape of the traveling wave. It's as if the swings were connected by ropes: the motion of one is transmitted to the others.
Such a simple model helps us understand how the ear copes with a huge range of loudness — from the rustle of leaves to the roar of an engine.
The cochlea is a spiral tube about 3.5 centimeters long, coiled into two and a half turns.
In the movie Osmosis Jones, sound is depicted as a wave traveling along a membrane, but in reality the ear actively amplifies weak signals, as in this model.