help (shape of very long rope full of TNT)

[jackthemack]

Let’s say we have a point ? on the ground at the coordinates (0,0). Assume that we are only operating on the ground plane (2D scenario). Someone puts a very long rope full of TNT with a certain shape around the point ?. ? is at one end of the rope. At the other end of the rope, the person ignites it. The fire advances through the rope at a constant speed ? and the explosions produce a soundwave with a constant celerity ?. What shape does the rope have if all the soundwaves arrived at ? at the exact same moment? In other words, find a function that can describe the curve that the rope takes.

 

[mmm4444bot]

rope full of TNT

That phrase makes no sense.

? is at one end of the rope … all the soundwaves arrived at ? at the exact same moment

How could that be possible, since the final sound wave originates at point O?
[imath]\;[/imath]

 

[blamocur]

That phrase makes no sense.


How could that be possible, since the final sound wave originates at point O?
[imath]\;[/imath]

In my interpretation the explosions happen everywhere along the rope's length and spread at constant speed ("celerity") 'c'.

 

[blamocur]

Let’s say we have a point ? on the ground at the coordinates (0,0). Assume that we are only operating on the ground plane (2D scenario). Someone puts a very long rope full of TNT with a certain shape around the point ?. ? is at one end of the rope. At the other end of the rope, the person ignites it. The fire advances through the rope at a constant speed ? and the explosions produce a soundwave with a constant celerity ?. What shape does the rope have if all the soundwaves arrived at ? at the exact same moment? In other words, find a function that can describe the curve that the rope takes.

A hint: at every point of the curve the angle between its tangent and the radial direction is the same.

 

[mmm4444bot]

In my interpretation the explosions happen everywhere along the rope's length

How would a continously-exploding rope maintain a fixed position? In your interpretation, how do you prevent the rope's shape from shifting, as it's blown to smithereens?
[imath]\;[/imath]

 

[blamocur]

How would a continously-exploding rope maintain a fixed position? In your interpretation, how do you prevent the rope's shape from shifting, as it's blown to smithereens?
[imath]\;[/imath]

It's math -- any assumption about real world is allowed

 

[AvgStudent]

How would a continously-exploding rope maintain a fixed position? In your interpretation, how do you prevent the rope's shape from shifting, as it's blown to smithereens?
[imath]\;[/imath]

Perhaps the Chinese firecrackers would make a bit more sense.

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