Reconstructing the Directivity Pattern of a Sound Source in Free Space by Measuring its Field in a Tank
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N ACOUSTICS. HYDROACOUSTICS
Reconstructing the Directivity Pattern of a Sound Source in Free Space by Measuring its Field in a Tank A. L. Virovlyanskya, *, A. Yu. Kazarovaa, and L. Ya. Lyubavina aInstitute
of Applied Physics of the Russian Academy of Sciences, Nizhny Novgorod, 603950 Russia *e-mail: [email protected] Received April 2, 2020; revised April 27, 2020; accepted April 28, 2020
Abstract—The paper discusses reconstruction of the directivity pattern of a sound source in free space from measurements of the field excited by this source in a tank. The reconstruction procedure uses a reference acoustic monopole. The field of the calibrated source is compared with the fields emitted by the monopole from several specially selected points of the tank. The signals of the source and reference monopole are recorded by the same receivers. From these measurements, the field of the source in the tank is approximated by superposing the fields of the acoustic monopoles. Conditions are formulated under which the field of the source in free space can be represented as the superposed fields of the same monopoles. This makes it possible to calculate the directivity pattern of the calibrated source in free space. The efficiency of the method is confirmed by numerical simulation results. Keywords: sound source, calibration, tank, equivalent source method DOI: 10.1134/S1063771020050152
1. INTRODUCTION AND FORMULATION OF THE PROBLEM Most methods for calibrating acoustic sources in a tank with reflecting boundaries isolate the direct signal arriving at the reception point without reflection from the boundaries. Very frequently, the boundaries are lined with an absorbing coating to dampen reflected signals and/or direct signals are isolated based on the propagation time [1, 2]. These approaches are effective only at sufficiently high frequencies. When calibrating low-frequency sources, the problem becomes complicated and its solution requires special signal processing methods [3–5]. In a recent work [6], an alternative approach was developed that allows calibration of a source in a tank without isolation of a direct signal. It uses the equivalent sources (ES) method [7–12]. It is assumed that the fields excited by the calibrated source both in the tank and free space can be represented as the superposed fields of the same acoustic monopoles, which play the role of ES with the same amplitudes. The amplitudes of ES are reconstructed from measurements in the tank. The values of the Green’s function for the Helmholtz equation needed to solve this inverse problem are measured using a procedure called tank calibration in [6]. In this procedure, the reference acoustic monopole is alternately placed at the ES location points and the signals emitted by it from these points are recorded by all receivers. The sought field of the source in free space is then easily calculated using
the found ES amplitudes and the well-known expression for the free-space Green’s function. The possibilities of this calibration method are significantly limited by
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