SPREADSHEET If you clap your hands at the end of a long,

Chapter , Problem 87

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SPREADSHEET If you clap your hands at the end of a long, cylindrical tube, the echo you hear back will not sound like the handclap; instead, you will hear what sounds like a whistle, initially at a very high frequency, but descending rapidly down to almost nothing. This culvert whistler is easily explained if you think of the sound from the clap as a single compression radiating outward from the hands. The echoes of the handclap arriving at your ear have traveled along different paths through the tube, as shown in Figure 16-37. The first echo to arrive travels straight down and straight back along the tube, while the second echo reflects once off of the center of the tube going out, and again going back, the third echo reflects twice at points and of the distance, and so on. The tone of the sound you hear reflects the frequency at which these echoes reach your ears. (a) Show that the time delay between the echo and the echo is where is the speed of sound, is the length of the tube, and is the tubes radius. (b) Using a spreadsheet program or graphing calculator, graph versus for (These values are the approximate length and radius of the long tube in the San Francisco Exploratorium.) Go to at least (c) From your graph, explain why the frequency decreases over time. What are the highest and lowest frequencies you will hear in the whistler?