I don't think particles are the way to go for this effect
If you are just looking for a 2D style animation you can easily do this with bezier curves and shapekyes or the offset property.
Just add a circle to your scene, duplicate it a few times (as many as desired) and scale them up a constant scale factor so they dist the same from each other.
Join them all into a single curve with Ctrl+J. Don't forget to apply the scale and reset all vertex radius into $1$ so they have the same weight.
Make all vertex handles type Free, then erase all segments leaving only a quarter circle. Rotate it $45º$ about the center and exit Edit Mode
Make a duplicate of your waves object for reference and make sure you add one additional wave outside the last one, again with the correct distance for snapping.
Now create two new shapekeys , one base and one for editing. In the editing one, scale all segments one by one so they reach exactly the one immediately after it with a bigger radius.
Make sure you scale with pivot on the 3D Cursor (period key .) and that the cursor is correctly placed at the center of the wave emission.
Animate the effect by keyframing the Factor property of your shapekeys with the i key, then make sure the animation curve handle is set to vector in the Graph Editor so the animation is smooth and without discontinuities.
Now add bevels and materials as desired
If you want a similar effect but with a 3D appearance and volumetric shape, then replace the bezier curves by 3D mesh spheres.
Bonus point if add a material with a gradient from color to transparent so the curves fade in and out at the ends.
I just found out a much easier way to achieve this, animate the Offset curve property instead, saves the trouble with all the shapekeys and scaling with references. Just create the concentric circles and join them together as before, but then just keyframe the Modification > Offset property instead.
Here is a bonus image with a possible node setup for the material. Add the gradient to transparency if you want it to fade away