Abdur Rahman

Date of Award


Degree Name

Master of Arts



First Advisor

Dr. Arthur McGurn

Second Advisor

Dr. E. Kamber

Third Advisor

Dr. Clement Burns

Access Setting

Masters Thesis-Open Access


In this thesis I study the band structure for acoustic waves propagating in a one-dimensional elastic array which forms a periodic elastic system in which band gaps are opened in the frequency spectrum. Specifically, I study the single impurity problem in this system. An impurity is introduced in the system by replacing one of the acoustic slabs with a new slab of different acoustic medium or by changing the thickness of impurity slab. I study the very narrow (in frequency) impurity modes in the band gaps which are localized about the impurity sites. Then I study the frequency of impurity modes as a function of thickness of impurity slab or impurity impedance, and determine what conditions are needed for an impurity mode to exist. The calculations presented in this thesis are based on numerically studying the transmittance of impurity modes into band gap in one-dimensional, periodic arrays of slabs.

Included in

Physics Commons