Inside a supersonic engine, there's a small recess in the wall, like a pocket. It's there to keep the flame from being blown out by the airflow, which moves faster than sound. But if you make the pocket long and shallow, it starts behaving like lungs: it pulls air in, then pushes it out. The frequency of this 'breathing' is 156 times per second. For the engine, it's like riding a bike with a wheel that keeps jerking.
Scientists filmed this pocket with an ultra-high-speed camera and measured pressure with special sensors. It turned out that the boundary between the fast flow outside and the slow air inside the pocket oscillates like a curtain in a draft. When the curtain bulges outward, the pressure in the pocket drops; when it bulges inward, the pressure rises. These two processes feed each other, so the oscillations don't die out on their own.
Now engineers know that for reliable engine operation, you need not only to cut the pocket correctly but also to heat the air inside it at the right time. Then, instead of vibrations, the pocket will calmly hold the flame, like a palm shielding a match from the wind.
The cavity 'breathing' frequency (156 Hz) is close to the idle rotation frequency of an automotive crankshaft, but the pressure oscillation amplitude reaches 30 kPa, comparable to the sound wave from a firecracker blast.