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This is a normal post OK, that's an interesting problem, let's see what I can come up with.
Firstly, the speed of sound you refer to is the speed of sound in free air. It simply measures the speed at which pressure waves are transmitted through an elastic medium, and is primarily dependent on the density of that medium. The density of a gas is governed by its temperature and pressure so let's just take the sea level value of ~340m/s for now and see where we end up. The speed of sound in the engine block will be in the region of 6000m/s so let's neglect that.

The pistons are the primary moving part to consider - they have the largest range of movement and therefore will displace the largest quantitiy of gas (indeed, that's what they're designed to do).

OK, so let's pick an engine to try. The Renault RS27 (PDF doc) powered Red Bull to the championship in 2013, the last season for the V8s. This revved over 18000 RPM. Unfortunately, what I can't find out is the piston stroke, so lets assume it's close to that of the V6 replacement's 53mm and call it 50mm (0.05m) for ease.

So:
- 18000 RPM gives 300 revs/sec.
- That gives a distance to cover of 300*0.05 = 15m

Therefore *on average* the piston is travelling at 15 m/s. Now at both ends of the stroke it's stationary or covering little distance, but even if we double the speed to 30m/s it's still travelling under 10% of the speed of sound in air.

------ tl;dr ------

Q: Is part of what we hear thousands of tiny sonic booms every second?
A: No.
(, Fri 26 Jun 2015, 20:14, , Reply)
This is a normal post I prefer the Milliband answer
"Hell Yes"!
(, Fri 26 Jun 2015, 22:29, , Reply)
This is a normal post THANK YOU FOR YOUR BRAIN

(, Sat 27 Jun 2015, 1:01, , Reply)
This is a normal post Rereading it this morning
I realise that, apart from it being a not entirely coherent explanation in desperate need of editing, I also cocked up the calculation:

The distance travelled by the piston during one cycle is double the stroke length. i.e. up and down the cylinder. That still doesn't get you anywhere near sonic velocities though, so doesn't change the conclusion.
(, Sat 27 Jun 2015, 9:16, , Reply)
This is a normal post You are Mona Lisa Vito AICMFP
www.youtube.com/watch?v=6qgREMBTE28
(, Sat 27 Jun 2015, 7:25, , Reply)
This is a normal post *Pays fiver*
*Strips naked and stands in front of mirror*

I want my money back!
(, Sat 27 Jun 2015, 9:20, , Reply)