The sonic passing bands and stopping gaps of a quasi-one-dimensional air tube with modulated mass density were studied experimentally and theoretically. Some gap modes whose wave functions are strongly localized near the ends of the air tube were also found. The simple experiment can be used as a demonstration of band structure in an upper-division physics course.
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Educational aids
REFERENCES
1.
D.
Griffiths
and C.
Steinke
, “Waves in locally periodic media
,” Am. J. Phys.
69
, 137
–154
(2001
).2.
E.
Yablonovitch
, J.
Gmitter
, and K.
Leung
, “Photonic band structure: The face-centered-cubic case employing nonspherical atom
,” Phys. Rev. Lett.
67
, 2295
–2298
(1991
).3.
S.
Parmley
, T.
Zobrist
, T.
Clough
, A.
Perez-Miller
, M.
Makela
, and R.
Yu
, “Phononic band structure in a mass chain
,” Appl. Phys. Lett.
67
, 777
–779
(1995
).4.
J.
Dowling
, “Sonic band structure in fluids with periodic density variations
,” J. Acoust. Soc. Am.
91
, 2539
–2543
(1992
).5.
C.
Bradley
, “Time harmonic acoustic Bloch wave propagation in periodic waveguides. I. Theory
,” J. Acoust. Soc. Am.
96
, 1844
–1853
(1994
);C.
Bradley
, “Time harmonic acoustic Bloch wave propagation in periodic waveguides. II. Experiment
,” J. Acoust. Soc. Am.
96
, 1854
–1862
(1994
).6.
P. Morse, Theoretical Acoustics (McGraw–Hill, New York, 1968).
7.
A. Fetter and J. Walecka, Theoretical Mechanics of Particles and Continua (McGraw–Hill, New York, 1980).
8.
The radial component of the velocity field satisfies the Bessel equation. The eigenfrequencies come from the boundary condition: where is the speed of sound in air (340 m/s), is the radius of the tube (0.072 m), and is the derivative of the -order Bessel function.
9.
D.
Sprung
, J.
Sigetich
, and H.
Wu
, “Bound states of a finite periodic potential
,” Am. J. Phys.
68
, 715
–722
(2000
).
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© 2002 American Association of Physics Teachers.
2002
American Association of Physics Teachers
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