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Expressing it mathematically becomes
L \propto \frac{1}{f}
As it varies, we change into equal sign and proportionality constant k:
L= k(\frac{1}{f})
Since L = 10 in and f = 512 cycles are the first conditions, the second one has L = 8 in with the unknown frequency. Because k is constant, equate the two conditions into one expression as
For f_2,
f_2= \frac{L_1f_1}{L_2}= \frac{(10in)(512cycles)}{8in}=640cycles

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