Sound Waves in a Medium Containing Rigid Spheres,
Abstract
The effective speed of sound is calculated for a medium containing immovable rigid spheres arranged in a simple cubic lattice. Long waves propagating along a lattice axis are treated. The wave equation for the pressure is reduced to an ordinary differential equation to which Floquet theory is applied. Both perturbation and numerical methods are use to find the effective speed as a function of frequency, and to locate the pass and stop bands. Two methods are presented for calculating the pressure, the phase velocity C and the propagation constant K for sound waves in a medium containing fixed rigid shperes arranged in a simple cubic lattice. One is a perturbation expansion in R/L, where R is the radium of a sphere and L is the distance between centers. The other is a direct numerical method. The results of the two methods agree well both when R/L is small and also when KL is small. The results show that there are pass bands and stop bands along the axis of kL = wL/C. The boundaries of the first three stop bands are given for five values of R/L. The values of C/c in the first two pass bands are given for five values of R/L and ten values of KL/pi. They show that C/c < or = 1 in the first pass band, and that C/c decreases as R/L increases and as KL increases. In the second band C/c > or = 1 except near the upper edge of the band. Within this band C/c still decreases as KL increases, but it increases as R/L increases.
Document Details
- Document Type
- Technical Report
- Publication Date
- Aug 01, 1986
- Accession Number
- ADA174669
Entities
People
- Dov Bai
- Joseph B. Keller
Organizations
- Stanford University