We consider the application of the lattice Boltzmann BGK model to simulate sound waves in situations where the density variation is small compared to the mean density. Linear sound waves are simulated in two different situations: a plane wave propagating in an unbound region; and a wave in a tube. For both cases the behaviour of the simulated waves is found to be in good agreement with analytic expressions. Non-linear sound waves are also simulated and are seen to display the expected features.
Methods of measuring the acoustic behavior of tubular systems can be broadly characterized as steady state measurements, where the measured signals are analyzed in terms of infinite duration sinusoids, and reflectometry measurements which exploit causality to separate the forward and backward going waves in a duct. This paper sets out a multiple microphone reflectometry technique which performs wave separation by using time domain convolution to track the forward and backward going waves in a cylindrical source tube. The current work uses two calibration runs ͑one for forward going waves and one for backward going waves͒ to measure the time domain transfer functions for each pair of microphones. These time domain transfer functions encode the time delay, frequency dependent losses and microphone gain ratios for travel between microphones. This approach is applied to the measurement of wave separation, bore profile and input impedance. The work differs from existing frequency domain methods in that it combines the information of multiple microphones within a time domain algorithm, and differs from existing time domain methods in its inclusion of the effect of losses and gain ratios in intermicrophone transfer functions.
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