Why does a cooling car engine crackle?
What determines the frequency of the crackles?
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I was told a long time ago that the sound is from "twinning" - this is where a metal under large stress experiences a reorientation of grains to relieve stress.
However I am not convinced this is the case - typically when the engine parts (catalytic converted being probably the hottest) cools down, it will shrink - and there is some "give" in the mountings that will cause it to slip when the tension gets high enough (this is sometimes referred to as "stick-slip"). The rate of clicking is then proportional to the rate of cooling, which is proportional to the temperature difference. So the rapid clicking says "hot", and as the clicking slows down, it indicates cooling.
It would be really fun to record the temperature and sound at the same time, and plot the temperature of the cat as a function of the frequency (1/interval between clicks). I don't have the setup - but hope someone reading this does...
As you drive, parts of the engine and exhaust system slowly heat up. They probably make cracking noises too, but you can't hear them over the sound of the engine and driving, and the noises-insulated driving cabin.
When you stop driving, they cool down, and the hot metal contracts causing a cracking sound.
the tink-tink-tink sound is stick-and-slip friction between different metal parts (mostly exhaust pipe components) that are bolted together. as they cool off, they contract at different rates depending on what they are made of and how fast they cool. Stresses build up in the joints between them until the static friction breaks into sliding friction; each time that break occurs you hear a tink.