Acoustics: Sound Fields, Transducers and Vibration, 2nd Edition

4.10. Radiation from a pulsating sphere

The pulsating sphere may be one of the most difficult sound sources to realize in practice, but it is the easiest three-dimensional source to analyze. Because of rotational symmetry, it can be treated as a one-dimensional problem with just a single radial ordinate r. Many practical sources behave in a similar way at low frequencies where they become virtually omnidirectional, as we shall see. Also, ultrasonic hydrosounders are often in the form of a sphere coated with a piezoelectric transducer. Essentially, the pulsating sphere is a sphere whose radius oscillates harmonically. In the limiting case, it will lead us to the point source, which forms a fundamental building block in acoustics.

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