Create and output a sound file using a sound file?

Suppose I have a sound file called clap.wav, and I want to export a sound file where clap.wav plays at certain timings. For clarification, here is an example with images captured using Audacity.

Let's say clap.wav is a sound file 0.111 seconds long.

I want to export a sound file where clap.wav plays at 0.000s, 0.300s, 0.550s and 0.600s.

The exported file should look like this. Take note that there is an overlap of the sounds played at 0.550s and 0.600s. That needs to be taken into consideration.

So, in a Java application, I already have an array of timings to have the sounds.

double timing[] = new double[]{0.0, 0.3, 0.55, 0.6}; //example

What do I have to do?