Beat (acoustics)/Just fifth displace stretch

First calculate $f_{B}$ using the beat period measured directly from the graph (then converting to frequency.)

$T_{B} = 8 T_{0} + 3 T_{x} = (6 \times 8 + 3 = 51) T_{x}$ $⟹ f_{B} = \frac{1}{51} f_{x}$ CHECK WITH BELOW

Now, check against the formula: $T_{B} = | p Δ f_{q} - q Δ f_{p} | :$

$Δ f_{p} = \frac{\tilde{N}}{\tilde{T}} - \frac{N}{T}$ , where $\frac{N}{T} = \frac{3}{6}$ (since there are 3 p-waves in time $T_{0}$ .)

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

$\tilde{T} = (8 \times 6 + 3) T_{x} = 51 T_{x}$ $⟹ \tilde{f_{p}} = \frac{25}{51} T_{x}$

$q Δ f = q | Δ f_{p} | = 2 | \frac{1}{2} - \frac{25}{51} | f_{x}$ $= (1 - \frac{50}{51}) f_{x} = \frac{1}{51} f_{x}$ THIS CHECKS WITH ABOVE

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