All Problems

Elastic Waves. Acoustics.

Problem 4.174

A source of sonic oscillations with frequency \(v_{0}=1000 \mathrm{~Hz}\) moves at right angles to the wall with a velocity \(u=0.17 \mathrm{~m} / \mathrm{s} .\) Two stationary receivers \(R_{1}\) and \(R_{2}\) are located on a straight line, coinciding with the trajectory of the source, in the following succession: \(R_{1}\) -source- \(R_{2}\) -wall. Which receiver registers the beatings and what is the beat frequency? The velocity of sound is equal to \(v=\) \(=340 \mathrm{~m} / \mathrm{s}\)

Reveal Answer
v=2v0vu/(v2u2)2v0u/v=1.0 Hzv=2 v_{0} v u /\left(v^{2}-u^{2}\right) \approx 2 v_{0} u / v=1.0 \mathrm{~Hz}