132
4 After the Lips: Acoustic Resonances and Radiation
Fig. 4.26 (a) Input impedance Z calculated for a cylindrical tube with length 2834 mm and radius
6.9 mm. (b) Z replotted with logarithmic axes. Peak envelopes are indicated by broken green lines
(Color figure online)
4.3.3 Conical Tubes
The propagation of sound waves in a conical tube is different from that in a
cylindrical tube in one important aspect: the waves travel not with plane wavefronts
but with spherical wavefronts. The nature of the wavefronts in a conical tube like
that shown by the dotted line in Fig. 4.22 can be visualised by drawing a small
circle on the surface of a partially inflated spherical balloon. The area of the balloon
surface inside the circle is not plane (flat), but bulges outwards in the centre. As the
balloon is inflated further, the area of the enclosed surface grows, just as the area of
the spherical wavefront grows during its progress along a conical tube.
4 After the Lips: Acoustic Resonances and Radiation
Fig. 4.26 (a) Input impedance Z calculated for a cylindrical tube with length 2834 mm and radius
6.9 mm. (b) Z replotted with logarithmic axes. Peak envelopes are indicated by broken green lines
(Color figure online)
4.3.3 Conical Tubes
The propagation of sound waves in a conical tube is different from that in a
cylindrical tube in one important aspect: the waves travel not with plane wavefronts
but with spherical wavefronts. The nature of the wavefronts in a conical tube like
that shown by the dotted line in Fig. 4.22 can be visualised by drawing a small
circle on the surface of a partially inflated spherical balloon. The area of the balloon
surface inside the circle is not plane (flat), but bulges outwards in the centre. As the
balloon is inflated further, the area of the enclosed surface grows, just as the area of
the spherical wavefront grows during its progress along a conical tube.