Page 20 - Spring 2010

DOWNLOAD THE KRAKATOA VIDEO CLIP
Shortly after the print copy of this issue is mailed, it will also be published in the Acoustical Society of America’s Digital Library. The Table of Contents may be reached direct- ly by going to your internet browser and typing the following Uniform Resource Locator (URL) in the address block: http://scitation.aip.org/dbt/dbt.jsp?KEY=ATCODK&Volum e=6&Issue=2. At some point in the download process you will probably be asked for your ID and Password if you are using a computer that is not networked to an institution with a subscription to the ASA Digital Library. These are the same username and password that you use as an ASA member to access the Journal of the Acoustical Society of America. Open the abstract for this article by clicking on Abstract. At the bot- tom of the abstract will be a link. Click on the link and a zipped folder (GabrielsonData.zip) will be downloaded to your computer (wherever you usually receive downlinks). Unzip the file. Open it and the video clip should play. (If it doesn’t start, click on the arrow icon. This clip does not have sound.) The video clip was recorded in QuickTime’s .MOV format. If you have difficulty in playing it, you might down- load the PC or MAC version of VLC Media Player from www.videolan.org. This is a non-profit organization that has created a very powerful, cross-platform, free and open source player that works with almost all video and audio formats. Questions? Email the Scitation Help Desk at help@scitation.org or call 1-800-874-6383.
tions to the view that the wave may be similar in nature to a long wave on the surface of the ocean. Much earlier, G. B. Airy (1845) showed that a surface wave on the ocean, if its wavelength is much larger than the ocean depth, would travel at a speed equal to the square root of the product of the ocean depth, h, and the acceleration of grav- ity, g. If the ocean-wave analogy is valid, the key to finding the speed of propagation in the atmosphere would be to find the effective height, h, of the atmosphere. The best guess was that the effective height is the height of a constant-density layer that produces the same surface pressure as the actual atmosphere.
John LeConte (1884) provides an interesting historical sidelight in his discussion of the propagation-speed argument. He paraphrases one of Newton’s expressions for the speed of sound in air: “the velocity of sound...[is] equal to that which a heavy body would acquire in falling vertically through half the height of the homoge- neous atmosphere whose...pressure
measures its elasticity.” (Newton’s expression is itself a counter- argument to those who claim that an explanation in words is always better than an equation!) LeConte notes that this reason- ing, if applied to the ocean, gives Airy’s result for the propagation speed of long-wavelength water waves.
However, in the case of water waves, Airy’s formula gives sur- face-wave propagation speeds far slower than the speed of propa- gation for compressional waves. For example, the tsunami pro- duced by the 2010 Chilean earthquake traveled the 6800 km from the epicenter to NDBC Buoy 43412 in 9 hours and 45 minutes for a speed of 193 meters per second. This implies an average water depth of 3800 meters, which is entirely reasonable given the path, but is far slower than the nearly 1500 meter per second speed of compressional acoustic waves in the ocean.
In contrast, Newton’s expression gives a speed only about 20 percent lower than the speed of ordinary acoustic waves in the atmosphere. (A constant-density atmosphere is, of course, ridiculous but if the surface pressure from a more realistic model with exponentially decreasing density is used to find the equivalent constant-density layer thickness, this thickness—the “scale height”—also produces the isothermal speed of sound.) The salient point here is that, for an ideal gas, the speed of sound calculated from the gas compressibility is close to the wave speed calculated from the long-surface-wave approxima- tion. Therefore, given the rudimentary state of knowledge con- cerning the vertical distribution of temperature in the atmos- phere, the fact that the Krakatoa pressure pulse traveled at a speed nearly equal to the ordinary speed of sound was evidence neither for nor against the pure acoustic nature of the wave.
Propagation calculations, even simplistic calculations based
16 Acoustics Today, April 2010
Fig. 4. Barograph traces from several stations for the first two passages of the wave (reproduced from Scott, 1883). All of these stations are in Europe. They show the first passage between 12:00 and 14:00 UTC on the 27th and the second passage between 04:00 and 06:00 on the 28th. The horizontal divisions are two hours apart. The vertical scale shown at the upper left represents one inch of mercury (about 3300 Pa).