How does a whip break speed of sound?

[d4rr3n]

I'm trying to understand by what mechanism a whip can multiply the velocity of the initial arm motion until it reaches the speed of sound, how is it doing this?

 

[mathman]

The end of the whip traces out a much longer distance than your arm, when going through one pass.

 

[nasu]

It has to do with the decreasing diameter of the whip, from the thick rope at the handle side to the very thin strands at he tip.
But the models to explain the details are not trivial.
A hand-waving explanation is the conservation of energy approach. As the whip becomes thinner, the same energy is distributed over a smaller mass so the speed of the whip particles increases. This is not wrong but it seems not to be the complete story.

 

[d4rr3n]

I have been watching slow motion videos of whips cracking and the tip makes a loop traveling at speeds above that of sound. I was thinking it might be due to centripetal acceleration. The radius of the loop decreases as it travels down the whip.

 

[fresh_42]

The mass m of the whip's part of the line which wants to become straight (the rest) is proportional to its length L. With L converges m to zero at constant kinetic energy E = 1/2·m·v². Due to energy conservation v increases to ∞. For practical reasons v is bounded but big enough to break the sound barrier.

 

[d4rr3n]

I have found that you can easily crack a leather cord with no tapering, therefore the belief that the phenomenon is due to the mass variance along the length of the whip is incorrect.

 

[fresh_42]

I have found that you can easily crack a leather cord with no tapering, therefore the belief that the phenomenon is due to the mass variance along the length of the whip is incorrect.

It's not the tapering, it's the throwback at the end of the line:

Without it, e.g. if you fix the end on the wall, you won't hear a bang.

 

[nasu]

I have found that you can easily crack a leather cord with no tapering, therefore the belief that the phenomenon is due to the mass variance along the length of the whip is incorrect.

Your "therefore" does not follow.
You can produce sound in many different ways. Most of them do not involve supersonic speeds.
If you look through the papers about the physics of the whip crack, you will see that the necessity of having supersonic speeds is not completely confirmed or accepted.
However the motion at speeds over speed of sound seem to be confirmed by both experiments and models.
The OP question was about what mechanism can explain the supersonic speeds and not about the relationship between these speeds and the whip crack.

 

[d4rr3n]

True Cause of Whip's Crack Uncovered
http://www.scientificamerican.com/article/true-cause-of-whips-crack/

In the above they are saying it is not the tip that brakes the speed of sound but it is the loop traveling down the whip which is accelerating until it exceeds the speed of sound.

"The crack of a whip comes from a loop traveling along the whip, gaining speed until it reaches the speed of sound and creates a sonic boom,"

In the video I posted you can see the loop that they are talking about and you can also see that the radius of the loop is decreasing as the speed is increasing.

 

[ycc_swe]

Here is an essay treating the physics of whipcracking. It explains the supersonic speed of the tip of the whip as a result of "a chain reaction of levers and blocks".
http://whip.creatingspeed.com