We experimentally demonstrate an avoided crossing in an acoustic system, consisting of two coupled PVC tube sections. One section has a fixed length, while the other has a variable length. Coupling between these tube sections is controlled by an aluminum diaphragm with a variable hole size. The avoided crossings in the acoustic system are compared to those of a quantum infinite square well split into two regions—one of fixed length and another of variable length. The two regions are separated by a delta potential well that controls the coupling between the two regions. We demonstrate that the acoustic and quantum systems exhibit similar avoided crossing behaviors.
References
1.
Luka
Novotny
, “Strong coupling, energy splitting, and level crossings: A classical perspective
,” Am. J. Phys.
78
, 1199
–1202
(2010
).2.
A.
Diaz-de-Anda
, K.
Volke-Sepúlveda
, J.
Flores
, C.
Sánchez-Pérez
, and L.
Gutiérrez
, “Study of coupled resonators in analogous wave systems: Mechanical, elastic, and optical
,” Am. J. Phys.
83
, 1012
–1018
(2015
).3.
Thomas
Faust
, Johannes
Rieger
, Mazimilan J.
Seitner
, Peter
Krenn
, Jörg P.
Kotthous
, and Eva M.
Weig
, “Non-adiabatic dynamics of two strongly coupled nanomechanical resonator modes
,” Phys. Rev. Lett.
109
, 037205
(2012
).4.
Jan R.
Rubbmark
, Micheal M.
Kash
, Micheal G.
Litman
, and Daniel
Kleppner
, “Dynamical effects at avoided level crossings: A study of the Landau-Zener effect using Rydberg atoms
,” Phys. Rev.
23
, 3107
–3117
(1981
).5.
K. R.
Brown
, C.
Ospeikaus
, Y.
Colombe
, A. C.
Wilson
, D.
Leibfreid
, and D. J.
Wineland
, “Coupled quantized mechanical oscillators
,” Nature
471
, 196
–199
(2011
).6.
Lee E.
Estes
, Thomas H.
Keil
, and Lorenzo M.
Narducci
, “Quantum-mechanical description of two coupled harmonic oscillators
,” Phys. Rev.
175
, 286
–299
(1968
).7.
David J.
Griffiths
, Introduction of Quantum Mechanics
(Prentice
, Upper Saddle River, NJ
, 1995
), p. 71
.8.
Shawn A.
Hilbert
and Herman
Batelaan
, “Acoustic analog to quantum mechanical level splitting
,” Am. J. Phys.
75
, 1003
–1008
(2007
).9.
Marissa
D'Onofrio
, Mitchell
Crum
, and Shawn A.
Hilbert
, “An acoustic analog to level splitting
,” Am. J. Phys.
84
, 841
–847
(2016
).10.
Reference 7, p. 73.
11.
Maxima is a computer algebra system, similar to Mathematica
. More information on Maxima can be found at <http://maxima.sourceforge.net>.12.
Stanford Research Systems function generator DS345
, <http://www.thinksrs.com/products/DS345.htm>.13.
CUI speaker CDM-10008 from Mouser Electronics
, <http://www.mouser.com/ProductDetail/CUI/CDM-10008/?qs=WyjlAZoYn50OuZNhzvXxYw%3D%3D>.14.
Kobitone microphone 254-ECM944-RO from Mouser Electronics
, <http://www.mouser.com/ProductDetail/Kobitone/254-ECM944-RO/?qs=jJIL5Dlg2FvxXdo8FTUk2A%3D%3D>.15.
Stanford Research Systems amplifier SR560
, <http://www.thinksrs.com/products/SR560.htm>.16.
Measurement Computing data acquisition board USB-204
, <https://www.mccdaq.com/usb-data-acquisition/USB-200-Series.aspx>.17.
Alessandra
Manzin
, Gabriele
Barrera
, Federica
Celegato
, Marco
Coïsson
, and Paola
Tiberto
, “Influence of lattice defects on the ferromagnetic resonance behaviour of 2D magnonic crystals
,” Sci. Rep.
6
, 22004
(2016
).© 2017 American Association of Physics Teachers.
2017
American Association of Physics Teachers
AAPT members receive access to the American Journal of Physics and The Physics Teacher as a member benefit. To learn more about this member benefit and becoming an AAPT member, visit the Joining AAPT page.