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Sonic boom may lag far behind breaking of the sound barrier

And, can speedy Achilles ever catch that slow tortoise?

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Question:Hearing a sonic boom, you look up and spot the plane. Does this mean it just "broke the sound barrier"?

Answer: It may have exceeded the speed of sound hours ago.

As a craft approaches Mach 1, sound waves racing out ahead can't get away fast enough so they "pile up" at the nose and trail off in the shape of a huge high pressure rearward cone. When this shock wave extends down far enough, groundlings hear it as a boom, but this may be long after the crossover point, like the wake of a ship touching shore.

When World War II aircraft neared Mach 1 during dives, they encountered buffeting and instability that led people to believe a "sound barrier" stood in the way of supersonic flight, says physicist Louis A. Bloomfield in "How Things Work." This was dispelled in October 1947 when Capt. Charles Yeager, flying with broken ribs from a horse-riding accident, took his XS-1 rocket plane to Mach 1.06 on a flight so uneventful he could only tell he had "slipped through" with the aid of instruments.

Question:Recap the timeworn linguistic sequence for a baby learning to "talk the talk."

Answer: Word No. 1, maybe "Mama" or "doggy," comes around birthday No. 1, soon followed by strings of gibberish then word No. 2, say John Darley et al. in "Psychology: 5th Edition." This is Baby's one-word-sentence stage, where "milk" might signify "I want more milk."

First 10 words will be names for animals, toys or foods, or anything big or moving or noisy. Not once in the first 50 words are you apt to hear the pragmatic "diaper," "sweater" or "mittens."

Usually by birthday No. 2, says Darley, Baby will begin forming two-word sentences, resembling telegraphic messages: "Hi, doggie," "More milk," "cookie allgone." There isn't any three-word-sentence stage. Loquacious Baby is starting to catch on now as utterances blossom in complexity. Next thing you know he or she will be saying things like, "I love you," "Can I have the car tonight?" and "Mom, I think I'm going to go for a Ph.D. in comparative linguistics."

Question:See if you can de-bug Zeno's famous Paradox, now 25 centuries old: Achilles runs 10 times as fast as a tortoise, which has a 10-meter head start in a race. While Achilles covers this 10 meters, the tortoise advances 1 meter. While Achilles covers this 1 meter, the tortoise advances another .1 meter. Etc. Every time Achilles catches up to where the tortoise was, the tortoise has moved ahead. Ergo, Achilles, though faster, can never catch up.

Answer: This defied analysis until the 1600s, says Isaac Asimov in his "Book of Facts," when Scottish mathematician James Gregory demonstrated "converging series" in which an infinite number of terms add up to a finite sum. Here the tortoise's 1 meter plus .1 meter plus .01 meter etc. converges to a sum of 1.11111111 . . . meter (1 1/9). That's exactly how far the slowpoke will get before he's passed up.


Send STRANGE questions to brothers Bill and Rich at strangetrue@compuserve.com