Problem 4.176

A receiver and a source of sonic oscillations of frequency \(v_{0}=2000 \mathrm{~Hz}\) are located on the \(x\) axis. The source swings harmonically along that axis with a circular frequency \(\omega\) and an amplitude \(a=50 \mathrm{~cm} .\) At what value of \(\omega\) will the frequency bandwidth registered by the stationary receiver be equal to \(\Delta v=200 \mathrm{~Hz} ?\) The velocity of sound is equal to \(v=340 \mathrm{~m} / \mathrm{s}\)