All Problems

Elastic Waves. Acoustics.

Problem 4.174

A source of sonic oscillations with frequency v0=1000 Hzv_{0}=1000 \mathrm{~Hz} moves at right angles to the wall with a velocity u=0.17 m/s.u=0.17 \mathrm{~m} / \mathrm{s} . Two stationary receivers R1R_{1} and R2R_{2} are located on a straight line, coinciding with the trajectory of the source, in the following succession: R1R_{1} -source- R2R_{2} -wall. Which receiver registers the beatings and what is the beat frequency? The velocity of sound is equal to v=v= =340 m/s=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}