Thursday, January 24, 2013

Digression on elephants and tsunami, a physics puzzle

Off topic, but I love puzzles.

This one is related to a story about elephants that came out of the 2004 Indonesian earthquake and tsunami.

In the story, a group of Indonesian work elephants became agitated and pulled up the stakes that supposedly held them tethered. They ran away from the sea, uphill, followed by their also very agitated human handlers. Shortly thereafter, the tsunami arrived ashore and the flood swept inland, but at lower elevation than the vantage point of the elephants and their attendants.

The social life and work attitudes of the elephants would be a delightful topic in itself, given their tolerance for being staked out as long as other things like food and safety were satisfactory.

But I also wanted to know more about when the elephants sensed there was danger.

Here's what might be a nice word problem for a promising freshman physics student.

Elephants can hear sounds as low as 14-18 Hertz frequency.
Tsunamis in the open ocean have far lower frequency than the range of elephant hearing (big hint),  a wavelength  can be 200 km, with a velocity of 800 kmh, and an amplitude that might be a few cm to a meter at most, not really noticeable to ships at sea.

When a tsunami approaches shallower water, it is compressed, so it slows down, reportedly to around 50 kmh, its wavelength shortens, and its frequency increases.    In terms of wave compression, like audible sound, the tsunami's pitch rises. With the compression at shallower water, the tsunami's wave amplitude also rises, sometimes to an astounding height.

Figure out the tsunami wavelength condition necessary for an elephant to be able to hear a tsunami coming.

If I knew the decibel sensitivity of an elephant at 14-18 Hz that would add to the fun.  There's a relatively old reference (Heffner and Heffner, 1982) that found a seven-year old female Indian elephant had a threshold of about 64 dB at 16 Hz.  Maybe there's more recent research.   In human terms 64 dB -  at an accessible frequency - could be an air conditioner or dishwasher, hardly as painful as an alarm. 

Then we'd want to know how far the tsunami was from the elephant, so we could guess what would be necessary in intensity for the elephants to react as if they'd heard an air-raid siren.  Did it even need to be loud, or just dangerously different?

It would also be credible to examine if the elephants had other modalities to sense danger. Did they feel something  unusual through their feet? Or even smell something strange as the sea pulled away from the shore..

June 11, 2013 Add in. Stanford University seismologists have suggested a tsunami warning system that uses sound cues from an earthquake.

"We've found that there's a strong correlation between the amplitude of the sound waves and the tsunami wave heights," co-author Eric Dunham, a Stanford geophysicist, said in a statement. "Sound waves propagate through water 10 times faster than the tsunami waves, so we can have knowledge of what's happening a hundred miles offshore within minutes of an earthquake occurring. We could know whether a tsunami is coming, how large it will be and when it will arrive."

Oh science is satisfying.

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