All Problems

Elastic Waves. Acoustics.

Problem 4.155

The equation of a travelling plane sound wave has the form ξ=60cos⁡(1800t−5.3x),\xi=60 \cos (1800 t-5.3 x), where ξ\xi is expressed in micrometres, tt in seconds, and xx 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.

Reveal Answer
 4.155. (a) a/λ=5.1⋅10−5;(b) vm=11 cm/s,3.2⋅10−4\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) (∂ξ/∂x)m=3.2⋅10−4,(∂ξ/∂t)m=v(∂ξ/∂x)m,(\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 km/sv=0.34 \mathrm{~km} / \mathrm{s} is the velocity of the wave.
Prev
Next