Beat (acoustics)/Just fifth displace stretch

Beat (acoustics)/header

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=(6\times 8+3=51)T_x$$⟹f_B=\frac{1}{51}{f}_x$ CHECK WITH BELOW

Now, check against the formula: $T_B=|p\mathrm{\Delta }{f}_q-q\mathrm{\Delta }{f}_p|:$

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

$\tilde{N}=(8\times 3)+1=25$

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

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