Being able to see where noise is generated and how it propagates would greatly simplify noise control strategy. Acoustic holography provides all acoustic variables including sound pressure, particle velocity, acoustic intensity and power. However, if we try to apply acoustic holography to the noise generated by moving noise sources, we must be able to measure the pressure on the moving plane affixed to the noise sources. This requires a very complex measurement system, e.g. a plane array of microphones, and therefore limits the practical applicability of acoustic holography to the case of moving noise sources.
A line array of microphones standing on the ground is obviously more practical than a plane array of microphones affixed to moving noise sources. Line array methods have been proposed to localize the noise sources of moving vehicles. The main objective of line array methods is to find the locations of the noise sources based on a beamforming method. These methods find an equivalent distribution of strengths of monopole sources over the source surface. This means that they cannot provide the way to describe how the wave front of noise propagates. It is also noteworthy that they cannot give us adequate information of sound pressure distribution, particle velocity, and acoustic intensity, all of which are obtainable from the acoustic holography method.
A practical method to visualize moving noise sources could combine the simplicity of the conventional line array methods and the flexibility of acoustic holography. Moving frame method was originally proposed to increase the aperture size of the hologram. In this method a line array of microphones continuously sweeps a sound field. The relative motion between the line array of microphones and the noise sources enables us to visualize the moving noise sources based on the acoustic holography method. If we have a line array of microphones standing on the ground, this method allows us to visualize the noise generated by moving sources based on acoustic holography. However, this method has inherent limitations due to the Doppler effect: The frequency band centered at a frequency of interest in the hologram coordinate is broadened as the relative speed between the noise source (hologram) and the line array of microphones is increased. Thus, this method is applicable only to tonal components, which rarely cause side band overlapping. The scope of practical application of moving frame method is limited due to this drawback. Note that moving noise sources have not only tonal components but also band-limited noise.
We propose an improved moving frame acoustic holography (MFAH) method so that we can apply it to the visualization of coherent band-limited moving noise sources.
Firstly, the applicability of moving frame method to the visualization of moving sources is analyzed theoretically. The movement of a noise source induces a change of wave front distribution of the radiated sound field. The wave fronts are closer together in the forward direction than they would be if the source were stationary. Therefore, the measured sound field by the microphone on the ground has an inherent error. The original radiation pattern and the position of the noise sources cannot be observed. We attempt to study this error and the way to reduce the error. A theoretical investigation is based on the assumption that we can express the sound field due to moving surface sources as a superposition of simple waves. This enables us to express the magnitude and the phase errors due to the moving effect on the hologram and the prediction plane explicitly. The analysis shows that the errors are mainly dependent on the speed of a noise source. It also assures the practical value of MFAH by showing that the errors are negligible if the speed of moving noise sources is much smaller than the speed of sound (M<0.1). A way of reducing the phase error on a hologram and a predicted sound field is also proposed.
Secondly, a method to visualize a band-limited noise is proposed. The proposed theory is based on the fact that a sound field can be expressed as a product of spatial and temporal functions. The measured signal by the relative motion between a line array of microphones and moving noise sources does not lose this property. Therefore, hologram (spatial function) can be obtained if the temporal function can be measured. In practice the temporal function can be measured by a reference microphone, which is fixed to the noise source. The applicability and limitation of the proposed method is analyzed by means of numerical simulations and experiments.
Thirdly, the practical applicability of the proposed method is discussed. The practical value of the proposed method is also illustrated by visualizing the noise generated by moving vehicle. The error due to the sideband overlapping is analyzed according to the speed, the frequency separation, and background noise. A method to apply the proposed method to the visualization of pass-by noise is proposed. The frequency change during the measurement was small enough to regard the radiated sound as stationary. The sound pressure and the intensity distribution of tire and engine noise during a pass-by test were obtained. The effect of running condition, e.g. cruising with constant speed, accelerating according to ISO362, and coasting down conditions, on the radiated sound were visualized.
