k-Wave Toolbox |

# mendousse

Compute Mendousse's solution for nonlinear waves propagation in viscous media

## Syntax

    p_mendousse = mendousse(x, t, source_freq, p0, c0, rho0, BonA, alpha_0)

## Description

`mendousse` calculates the propagation of a monofrequency plane wave source in thermoviscous medium with absorption given by `alpha_0*f^2`. The solution is taken from Eq. (264) in Chapter 4 of Nonlinear Acoustics by Hamilton and Blackstock (2008). The infinite sum is adaptively truncated when the moving average of the previous five sum terms is smaller than a predefined convergence percentage (0.01 percent by default). An example of using the function is given below.

    % define the properties used in the simulation
    source_freq = 1e6;      % [Hz]
    p0 = 5e6;               % [Pa]
    c0 = 1500;              % [m/s]
    rho0 = 1000;            % [kg/m^3]
    BonA = 12;
    alpha_0 = 0.5;          % [dB/(MHz^2 cm)
    x = 0:75e-6:40e-3;      % [m]
    t = x./c0;              % [s]

    % compute solution
    p_mendousse = mendousse(x, t, source_freq, p0, c0, rho0, BonA, alpha_0);

    % plot
    figure;
    plot(x*1e3, p_mendousse/1e6);
    ylabel('Pressure [MPa]');
    xlabel('Distance [mm]');

## Inputs

`x` | position [m]
`t` | time [s]
`source_freq` | frequency of plane wave [Hz]
`p0` | source pressure [Pa]
`c0` | medium sound speed [m/s]
`rho0` | medium density [kg/m^3]
`BonA` | nonlinearity parameter B/A
`alpha_0` | absorption coefficient [dB/(MHz^2 cm)]

## Outputs

`p_mendousse` |

## Examples

- Modelling Nonlinear Wave Propagation

## See Also

`randn`

© 2009, 2010, 2011 Bradley Treeby and Ben Cox.