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Elastic Waves. Acoustics.

Problem 4.187

A point AA is located at a distance r=1.5 mr=1.5 \mathrm{~m} from a point isotropic source of sound of frequency v=600 Hz.v=600 \mathrm{~Hz} . The sonic power of the source is P=0.80 WP=0.80 \mathrm{~W}. Neglecting the damping of the waves and assuming the velocity of sound in air to be equal to v=340 m/sv=340 \mathrm{~m} / \mathrm{s} find at the point AA : (a) the pressure oscillation amplitude (Δp)m(\Delta p)_{m} and its ratio to the air pressure; (b) the oscillation amplitude of particles of the medium; compare it with the wavelength of sound.

Reveal Answer
4.187. (a) (Δp)m=ρvP/2πr2=5 Pa,(Δp)m/p=5⋅10−5;(\Delta p)_{m}=\sqrt{\rho v P / 2 \pi r^{2}}=5 \mathrm{~Pa}, \quad(\Delta p)_{m} / p=5 \cdot 10^{-5} ; (b) a=(Δp)m/2πvρv=3μm,a/λ=5⋅10−6a=(\Delta p)_{m} / 2 \pi v \rho v=3 \mu m, a / \lambda=5 \cdot 10^{-6}
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