Acoustic and quantum-mechanical analogues to the problem of a loaded string fixed at both ends

• Published in: European journal of physics Vol. 30; no. 5; pp. 1107 - 1117
• Main Authors: Gómez, B J, Repetto, C E, Stia, C R, Welti, R
• Format: Journal Article
• Language: English
• Published: Bristol IOP Publishing 01.09.2009; Institute of Physics
• Subjects: Communication, education, history, and philosophy; Exact sciences and technology; General physics; Physics; Physics literature and publications; Surveys and tutorial papers, resource letters; Band structure; Higher education; Quantum wells; Potential function; Resonance; Physics; Delta function
• ISSN: 0143-0807; 1361-6404
• DOI: 10.1088/0143-0807/30/5/017

In this paper we study an acoustic system comprised of two identical closed tubes connected with a short one, and a quantum-mechanical square well with a delta function potential. Both systems can be thought of as mathematically equivalents to the homogeneous string with a concentrated mass at its middle point. We describe also a simple experimental device to measure the resonances of the acoustic system as a function of the connecting tube section. The experimental setup and the theoretical approach we have employed can be used in both undergraduate and graduate level courses. Moreover, this work may be useful as a teaching aid in other experimental research projects such as for instance the study of the emergence of the band structure in solid state physics.