Beat (acoustics)/Just fifth displace stretch

A wild-goose chase

First calculate $$f_B$$ using the beat period measured directly from the graph (then converting to frequency.)

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

Now, check against the formula: $$T_B=\left|p\Delta f_q - q\Delta f_p\right|:$$

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

$$\widetilde N = (8\times 3) + 1 = 25$$

$$\widetilde T = (8\times 6 + 3)T_x=51T_x$$$$\implies \widetilde {f_p} =\frac{25}{51}T_x$$

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