View source for Beat (acoustics)/Just fifth displace stretch

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A [[wikt:wild-goose chase|wild-goose chase]]

First calculate <math>f_B</math> using the beat period measured directly from the graph (then converting to frequency.)

<math>T_B=8T_0+3T_x= \left(6\times 8+ 3 = 51\right)T_x</math><math>\implies f_B=\frac{1}{51}f_x</math> CHECK WITH BELOW

Now, check against the formula: <math>T_B=\left|p\Delta f_q - q\Delta f_p\right|:</math>

<math>\Delta f_p = \frac {\widetilde N}{\widetilde T} - \frac N T</math>, where <math>\frac N T = \frac 3 6 </math> (since there are 3 p-waves in time <math>T_0</math>.)

<math>\widetilde N = (8\times 3) + 1 = 25</math> 

<math>\widetilde T = (8\times 6 + 3)T_x=51T_x</math><math>\implies  \widetilde {f_p} =\frac{25}{51}T_x</math>

<math>q\Delta f = q\left|\Delta f_p\right|=2\left|\frac 1 2 -\frac{25}{51}\right|f_x</math> <math>=\left(1-\frac{50}{51}\right)f_x=\frac{1}{51}f_x</math> THIS CHECKS WITH ABOVE





[[File:Just fifth displace stretch.svg|900px]]