How much sound in an airplane crash?

[Tio Barnabe]

I'm engaged in a discussion with a friend about how loud is the sound of an airplane crashing into the ground. I'm considering that the sound wave produced is roughly spheric. I need to know how much (percent) of the kinetic energy the airplane has before hitting the ground is converted into sound energy? Is it safe to consider ~ 10% for a commercial airplane?

 

[berkeman]

I'm engaged in a discussion with a friend about how loud is the sound of a airplane crashing into the ground. I'm considering that the sound wave produced is roughly spheric. I need to know how many (percent) of the kinetic energy the airplane has before hitting the ground is converted into sound energy? Is it safe to consider ~ 10% for a commercial airplane?

It's probably similar to the % of the KE when a NASCAR race car crashes head on into a wall. The sound energy seems like it would be more like in the 1% range. (Not counting the explosion that often accompanies a plane crash soon after impact).

 

[Tio Barnabe]

Now the total area of the sound wave would not be $4 \pi r^2$ because the ground blocks off half the wave. So should I consider the area as being $2 \pi r^2$?

 

[berkeman]

Now the total area of the sound wave would not be $4 \pi r^2$ because the ground blocks off half the wave. So should I consider the area as being $2 \pi r^2$?

That seems reasonable. You might be able to search for car crash videos with sound to get an idea of the sound intensity at different distances. The sound might be enhanced in the videos, though, so you would have to exercise your judgement on how accurate the sound levels were. Have you calculated the typical KE of a car at freeway speeds? How does that compare to the energy in that expanding sound wave? It would seem like the KE of the car moving so quickly would be huge to the sound energy emitted by the crash. And remember that the car/plane KE goes up as the speed squared...

 

[Tio Barnabe]

Good idea. I will look for such videos. But, on the other hand, the part of the wave that doesn't goes out, is dissipated on the soil. So it seems just equivalent to consider that less percent of the total energy of the plane goes to produce the sound wave -as opposed to the case where there's no soil- and continue considering $4 \pi r^2$ as the area. What do you think of this?

 

[berkeman]

Good idea. I will look for such videos. But, on the other hand, the part of the wave that doesn't goes out, is dissipated on the soil. So it seems just equivalent to consider that less percent of the total energy of the plane goes to produce the sound wave -as opposed to the case where there's no soil- and continue considering $4 \pi r^2$ as the area. What do you think of this?

I don't know, TBH. But it seems like some of the downward-directed sound energy of the crash would reflect and become part of the rising sound hemisphere...

 

[jbriggs444]

Vibrations in soil and fuselage couple only poorly to the air. Consider, for instance, a tuning fork. It couples so poorly to the air that it continues vibrating for multiple seconds before dissipating significant energy. By contrast, the vibration of a crashing car or aircraft damps out almost immediately. It does not ring.

From this, I would conclude that most of the energy is damped into heat and vibrations in the soil.

 

[CWatters]

Perhaps look for reports of aircraft crashes being heard X miles away?