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Elastic Waves. Acoustics.

Problem 4.176

A receiver and a source of sonic oscillations of frequency v0=2000 Hzv_{0}=2000 \mathrm{~Hz} are located on the xx axis. The source swings harmonically along that axis with a circular frequency ω\omega and an amplitude a=50 cm.a=50 \mathrm{~cm} . At what value of ω\omega will the frequency bandwidth registered by the stationary receiver be equal to Δv=200 Hz?\Delta v=200 \mathrm{~Hz} ? The velocity of sound is equal to v=340 m/sv=340 \mathrm{~m} / \mathrm{s}

Reveal Answer
ω=v0vaΔv(1+(Δv/v0)2−1)=34 s−1\omega=\frac{v_{0} v}{a \Delta v}\left(\sqrt{1+\left(\Delta v / v_{0}\right)^{2}}-1\right)=34 \mathrm{~s}^{-1}
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