All Problems Elastic Waves. Acoustics.
Problem 4.155
The equation of a travelling plane sound wave has the form \(\xi=60 \cos (1800 t-5.3 x),\) where \(\xi\) is expressed in micrometres, \(t\) in seconds, and \(x\) in metres. Find: (a) the ratio of the displacement amplitude, with which the particles of medium oscillate, to the wavelength; (b) the velocity oscillation amplitude of particles of the medium and its ratio to the wave propagation velocity; (c) the oscillation amplitude of relative deformation of the medium and its relation to the velocity oscillation amplitude of particles of the medium.
\(\begin{array}{llll}\text { 4.155. (a) } a / \lambda=5.1 \cdot 10^{-5} ; & \text {(b) } v_{m}=11 & \mathrm{~cm} / \mathrm{s}, & 3.2 \cdot 10^{-4}\end{array}\) (c) \((\partial \xi / \partial x)_{m}=3.2 \cdot 10^{-4},(\partial \xi / \partial t)_{m}=v(\partial \xi / \partial x)_{m},\) where \(v=0.34 \mathrm{~km} / \mathrm{s}\) is the velocity of the wave.