The Neumann boundary value problem for the Helmholtz equation within the quarter-space has been considered in this paper. The Green function has been used to find the acoustic pressure amplitude as the approximation valid within the Fraun-hoffer's zone for some time-harmonic steady state processes. The low fluid loading has been assumed and the acoustic attenuation has been neglected. It has also been assumed that the vibration velocity of the acoustic particles is small as compared with the sound velocity in the gaseous medium.

Sound propagation from the vehicles moving on the city roundabout, with taking into account the wind is investigated. Solution of the problem for one moving sound source is found by means of the integral Fourier transforms extended over space variables and time. Inverse transforms are calculated approximately, using a stationary phase method and iterative technique. The solution for a general problem is obtained as a superposition of many partial solutions. The numerical analysis of noise characteristics is performed for the three-way Korfanty roundabout case in Łódź.

In many therapeutic applications of a pulsed focused ultrasound with various intensities the finite- amplitude acoustic waves propagate in water before penetrating into tissues and their local heating. Water is used as the matching, cooling and harmonics generating medium. In order to design ultrasonic probes for various therapeutic applications based on the local tissue heating induced in selected organs as well as to plan ultrasonic regimes of treatment a knowledge of pressure variations in pulsed focused nonlinear acoustic beams produced in layered media is necessary. The main objective of this work was to verify experimentally the applicability of the recently developed numerical model based on the Time- Averaged Wave Envelope (TAWE) approach (Wójcik et al., 2006) as an effective research tool for predicting the pulsed focused nonlinear fields produced in two-layer media comprising of water and tested materials (with attenuation arbitrarily dependent on frequency) by clinically relevant axially-symmetric therapeutic sources. First, the model was verified in water as a reference medium with known linear and nonlinear acoustic properties. The measurements in water were carried out at a 25◦C temperature using a 2.25 MHz circular focused (f/3.0) transducer with an effective diameter of 29 mm. The measurement results obtained for 8-cycle tone bursts with three different initial pressure amplitudes varied between 37 kPa and 113 kPa were compared with the numerical predictions obtained for the source boundary condition parameters determined experimentally. The comparison of the experimental results with those simulated numerically has shown that the model based on the TAWE approach predicts well both the spatial-peak and spatial-spectral pressure variations in the pulsed focused nonlinear beams produced by the transducer used in water for all excitation levels complying with the condition corresponding to weak or moderate source-pressure levels. Quantitative analysis of the simulated nonlinear beams from circular transducers with ka ≫ 1 allowed to show that the axial distance at which sudden accretion of the 2nd or higher harmonics amplitude appears is specific for this transducer regardless of the excitation level providing weak to moderate nonlinear fields. For the transducer used, the axial distance at which the 2nd harmonics amplitude suddenly begins to grow was found to be equal to 60 mm. Then, the model was verified experimentally for two-layer parallel media comprising of a 60-mm water layer and a 60-mm layer of 1.3-butanediol (99%, Sigma-Aldrich Chemie GmbH, Steinheim, Germany). This medium was selected because of its tissue-mimicking acoustic properties and known nonlinearity parameter B/A. The measurements of both, the peak- and harmonic-pressure variations in the pulsed nonlinear acoustic beams produced in two-layer media (water/1.3-butanediol) were performed for the same source boundary conditions as in water. The measurement results were compared with those simulated numerically. The good agreement between the measured data and numerical calculations has shown that the model based on the TAWE approach is well suited to predict both the peak and harmonic pressure variations in the pulsed focused nonlinear sound beams produced in layered media by clinically relevant therapeutic sources. Finally, the pulsed focused nonlinear fields from the transducer used in two-layer media: water/castor oil, water/silicone oil (Dow Corning Ltd., Coventry, UK), water/human brain and water/pig liver were predicted for various values of the nonlinearity parameter of tested media.

The sound radiation from vehicles travelling on the city roads with T junction was considered. The wind effect on acoustic field was taken into account. The solution of this problem was found with the help of the integral Fourier transforms and stationary phase method as the superposition of solutions for the cases of vehicles moving along the straight roads and roads with right-angle bend. As an example, the numerical analysis of traffic noise characteristics was carried out for the T junction city road on one of streets in the town of Łodź (Poland).