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Elastic Waves. Acoustics.

Problem 4.184

An observer \(A\) located at a distance \(r_{A}=5,0 \mathrm{~m}\) from a ringing tuning fork notes the sound to fade away \(\tau=19 \mathrm{~s}\) later than an observer \(B\) who is located at a distance \(r_{B}=50 \mathrm{~m}\) from the tuning fork. Find the damping coefficient \(\beta\) of oscillations of the tuning fork. The sound velocity \(v=340 \mathrm{~m} / \mathrm{s}\).

Reveal Answer
β=ln⁡(rB/rA)/[τ+(rB−rA)/v]=0.12 s−1\beta=\ln \left(r_{B} / r_{A}\right) /\left[\tau+\left(r_{B}-r_{A}\right) / v\right]=0.12 \mathrm{~s}^{-1}
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