Speed of Sound in a Rod
Date: 07/05/99 at 23:00:39 From: Tyler Johnson Subject: Sound speed Dr. Math, I am a home-schooler and this is a question that is on my exit exam so I can graduate. Neither of my parents knows where to start or how to explain it. Therefore if it is possible, can you explain or give the formula needed instead of just the answer? The problem is: The speed of sound in an iron rod is 16,850 ft/sec, and the speed in air is 1100 ft/sec. If a sound originating at one end of the rod is heard in the rod one second before it is heard in the air, how long is the rod? Thank you for looking at this. Sincerely, Tyler Johnson
Date: 07/06/99 at 15:38:18 From: Doctor Fwg Subject: Re: Sound speed Dear Tyler, Try the problem this way: The distance is the same in both cases. Let that distance be D. The time for the sound to travel through the rod is Tr. The time for the sound to travel through the air is Ta. The velocity of sound in the rod is 16,850 ft/sec. The velocity of sound in air is 1100 ft/sec. But, Ta = Tr + 1 (Note: Ta is longer than Tr.) And, D = VrTr = VaTa = Va(Tr + 1) so: VrTr = Va(Tr + 1). Therefore: Vr/Va = (Tr + 1)/Tr = 16,850/1100 = 15.318 so: (Tr + 1)/Tr = 15.318. Next, solve for Tr, then plug into the equation: D = VrTr to get D. I hope this helps. With best wishes, - Doctor Fwg, The Math Forum http://mathforum.org/dr.math/
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