Hi Kevin,

Excellent question. There is a reason for the behaviour you see.

When your source is a single point in time, eg. `source.p = 1`

, then the time series you measure at your detector will be the impulse response function. What this actually is will depend on the numerical method you are using. In k-Wave, for a homogeneous medium, you will see the convolution of the Green's function for the wave equation and the band-limited interpolant, see Section 2.8 in the manual. (What this looks like will depend on how many spatial dimensions you are working in.)

When your source has two points in time, eg. `source.p = [1 1]`

, then what you will see will be the sum of two copies of the impulse response function spaced by `dt`

in time. Usually `dt`

is short enough that the two impulse responses will not be clearly separable, but will form an output with a single maximum, but at a higher level. (A useful exercise is to plot the measured time series as you increase the spacing between two pulses: `source.p = [1 0 0 ... 0 0 1]`

. Eventually the two pulses measured at the detector will become separated in time.)

Adding increasing numbers of time points to the source, `source.p = [1 1 1 ... ]`

, will continue to increase the maximum value of the output (well, there are some small oscillations) until eventually it settles down to a steady value. (Another useful exercise is to plot the maximum of the measured time series as a function of the number of pulses used in `source.p`

.)

So there are essentially two different regimes in which the 'source amplitude' is well-defined: a single pulse and a sufficiently long train of pulses. When using `source.p`

, k-Wave by default scales the output so a plane wave excited by a long train of pulses will have the same amplitude as the source. When setting an initial value problem using `source.p0`

k-Wave does not include the scaling factor, so that, again, the output is in the same units as the initial pressure distribution.

Spreading the source spatially can help ameliorate this effect (see Manual, Figure 2.6).

Hope that helps,

Ben