Dropping a rock down a deep hole
Jearl Walker  www.flyingcircusofphysics.com
May 2013  Scary things are fascinating things. Maybe that is why I am fascinated by really deep holes in the ground --- I can imagine myself falling down the shaft like Alice falling into the rabbit hole and landing in a mystical world.

Here is a video of a 450 m shaft that had been drilled vertically downward into a mountain side in order to drain a lake into a lower lake. Listen to the sound of the rock landing at the bottom.

http://wimp.com/deepesthole/

http://www.youtube.com/watch?v=2czbp9V9F4A same video

The intention of the shaft was to drive a hydroelectric plant. Once the shaft was completed, the area around the hole was filled to form a small lake, with a valve that could prevent the water from flowing through the shaft. During the day, the valve is turned so that water falls down the shaft and into a lower lake. The flow drives the plant generators so that electricity is produced during the peak demand. At night when the demand is much less, electricity is used to pump the water back up to the higher lake, to be ready for the next day. Although that pumping is expensive, the cost is much less than the profit the company makes during the peak demand.

An explanation, along with an animation, is in one of the videos at the following site. Search there for “Throwing a rock down a 1500 ft hole; how and why it was made”.

http://www.youtube.com/user/fredrikjohansson#p/u/0/2czbp9V9F4A .

You can approximate the depth of a hole by measuring the time between the release of a stone into the hole and the instant the sound of its final impact reaches you. That time interval is the total of the time for the stone to fall and the time for the sound of the impact to travel back up to you. Both times involve the depth of the hole.

If we make the assumption that the stone free falls (without being slowed by ricocheting from the wall), the time required to fall to depth d (in meters) is

t1 = square root (d/4.9 m/s^2).

The time for sound to travel back up the hole at the typical speed of 343 m/s is

t2 = d/(343 m/s).

For example, if the total time turns out to be 11 s as in the video, then the depth is about 450 m.

Here is an even more extreme example, in which the total time is 35 s. Again under the assumption of free fall, the depth is about 3.2 km.

https://www.youtube.com/watch?v=ILDD9vyNeN0

This hole is located near the Dugway Proving Grounds in west Utah. The people who shot the video conducted several experiments in addition to dropping the stone, including lowering a rock on a 1000 foot fishing line, which was not long enough to reach bottom.

I have one more video, a deep hole in Israel, but I must warn you that a medium-level curse word is uttered by one of the young men in astonishment about the depth of the hole. What caught my attention with this video is the sound made by the falling stone. We do not hear the dull thudding as in the previous video. Instead we hear a zinging sound, which is known as a whistler.

Normally I can demonstrate a whistler with a handclap at the end of a long pipe or culvert, with you at the other end. You hear a series of echoes, one involving a single reflection from the interior wall, another involving two reflections, and so on. Each extra reflection means that the associated sound takes a longer path to reach you and thus there is a delay in that echo. So, you hear a series of echoes --- the whistler.

As the stone falls in this last hole, each collision with the wall sends a series of echoes back up the hole, and so we hear multiple whistlers.

http://www.youtube.com/watch?v=JT-INK5yHLA rude word used

References
Dots · through ··· indicate level of difficulty
Journal reference style: author, journal, volume, pages (date)
··· Crawford, F. S., “Culvert whistlers,” American Journal of Physics, 39, 610-615 (June 1971)
· Rinard, P. M., “Rayleigh, echoes, chirps, and culverts,” American Journal of Physics, 40, 923-924 (June 1972)
· Pizzo, J. “Echo tube,” Physics Teacher, 24, No. 7, 429-430 (October 1986)
·· Crawford, F. S., “Culvert whistlers revisited,” American Journal of Physics, 56, No. 8, 752-754 (August 1988)
· Simpson, A. M., and S. R. Ryan, “Racquetball court whistlers,” American Journal of Physics, 59, No. 2, 175-176 (February 1991)
··· Adler, C. L., K. Mita, and D. Phipps, “Quantitative measurement of acoustic whistlers,” American Journal of Physics, 66, 607-612 (July 1998)
·· Karlow, E. A., “Culvert whistlers: harmonizing the wave and ray models,” American Journal of Physics, 68, No. 6, 531-539 (June 2000)