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Elastic Waves. Acoustics.

Problem 4.175

A stationary observer receives sonic oscillations from two tuning forks one of which approaches, and the other recedes with the same velocity. As this takes place, the observer hears the beatings with frequency \(v=2.0 \mathrm{~Hz}\). Find the velocity of each tuning fork if their oscillation frequency is \(v_{0}=680 \mathrm{~Hz}\) and the velocity of sound in air is \(v=340 \mathrm{~m} / \mathrm{s}\)

Reveal Answer
u=vv0v(1+(v/v0)2−1)≈vv2v0=0.5 m/su=\frac{v v_{0}}{v}\left(\sqrt{1+\left(v / v_{0}\right)^{2}}-1\right) \approx \frac{v v}{2 v_{0}}=0.5 \mathrm{~m} / \mathrm{s}
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