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Unformatted text preview: 65. The points and the leastsquares ﬁt is shown in the graph below. The graph has frequency in Hertz
along the vertical axis and 1/L in inverse meters along the horizontal axis. The function found by the
least squares ﬁt procedure is f = 276(1/L) + 0.037. Assuming this ﬁts either the model of an open
organ pipe (mathematically similar to a string ﬁxed at both ends) or that of a pipe closed at one end,
as discussed in the textbook, then f = v/2L in the former case or f = v/4L in the latter. Thus, if the
leastsquares slope of 276 ﬁts the ﬁrst model, then a value of v = 2(276) = 553 m/s is implied. In the
second model (the pipe with only one end open) we ﬁnd v = 4(276) = 1106 m/s which is more “in the
ballpark” of the 1400 m/s value cited in the problem. This suggests that the acoustic resonance involved
in this situation is more closely related to the n = 1 case of Figure 1815(b) than to Figure 1814.
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frequency 20
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0.02 0.04 0.06
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reciprocal_L 0.1 0.12 ...
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 Fall '08
 SPRUNGER
 Physics

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