A Primer on Quantum Fluids by Carlo Barenghi & Nick G. Parker

Author:Carlo Barenghi & Nick G. Parker
Language: eng
Format: epub
Publisher: Springer International Publishing, Cham

4.1.2 Sound Waves

For repulsive interactions () and in the limit of small k/long waves, the above dispersion relation predicts waves whose angular frequency increases linearly with wavenumber. This is characteristic of sound waves. The phase velocity of these waves is , which is approximately constant for all wavelengths. This defines the speed of sound,

(4.6)

The physical interpretation of these waves is readily obtained using the Madelung transform. By perturbing the state of uniform density , we obtain the one-dimensional wave equation,

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