# Acoustic scattering

In many fields of acoustics as ultrasound imaging, NDT or submarine acoustics, the knowledge of the reflected field of even simple scatterers are needed to understand the information of the reflections of these bodies. Thus, here we show a simple scattering example by a rigid cylinder. The following images shows the incident, total and reflected field of the scatterer. The complex reflected field can be calculated simply as:

\[\hat{P_r}=\hat{P_t}-\hat{P_i}\]

where \(\hat{P_r}\) is the reflected field, \(\hat{P_i}\) is incident and \(\hat{P_t}\) is the total measured acoustic field for a cylinder of radius \(R\) and a incident field of wavelength \(\lambda\).

## Scattering by a cylinder of \(R /\lambda=0.35\)

These three images are the modulus of the complex value of the pressure (i.e. the envelope the measured time domain field) for a rigid cylinder of \(R /\lambda=0.35\) for the incident pressure field \(\hat{P_i}\), the total field \(\hat{P_t}\) and finally the computed reflected field \(\hat{P_r}\).

The below three images are the distribution of the real part of the pressure (i.e. physical pressure you have for a fixed time) for the incident pressure field \(\hat{P_i}\), the total field \(\hat{P_t}\) and finally the computed reflected field \(\hat{P_r}\).

## Scattering by a cylinder of \(R /\lambda=1\)

These three images are the modulus of the complex value of the pressure (i.e. the envelope the measured time domain field) for a rigid cylinder of \(R /\lambda=1\) for the incident pressure field \(\hat{P_i}\), the total field \(\hat{P_t}\) and finally the computed reflected field \(\hat{P_r}\).

The below three images are the distribution of the real part of the pressure (i.e. physical pressure you have for a fixed time) for the incident pressure field \(\hat{P_i}\), the total field \(\hat{P_t}\) and finally the computed reflected field \(\hat{P_r}\).

## Scattering by a cylinder of \(R /\lambda=2\)

These three images are the modulus of the complex value of the pressure (i.e. the envelope the measured time domain field) for a rigid cylinder of \(R /\lambda=2\) for the incident pressure field \(\hat{P_i}\), the total field \(\hat{P_t}\) and finally the computed reflected field \(\hat{P_r}\).

The below three images are the distribution of the real part of the pressure (i.e. physical pressure you have for a fixed time) for the incident pressure field \(\hat{P_i}\), the total field \(\hat{P_t}\) and finally the computed reflected field \(\hat{P_r}\).