How to scale an object and at same time fix the position ?

I'm trying to make a signal that expand like normal signal and move forward with the speed of sound ...
this is for research helping my prof. to simulate this thing ...
i tried to use local scale but always changing the position of my object over time ...

Code (CSharp):

1.  gameObject.transform.localScale +=new Vector3(0.3f,0.3f,0.3f);
2.  
3.  gameObject.transform.position += new Vector3(_x, _y, _z);

please help

my prefap: https://drive.google.com/file/d/1nvgbHgNpOX6mPn76H3c2LfWfG8rYy9I1/view?usp=sharing

 

Parent it to an empty object in such way that the parent is located at the point from which the object should expand, and scale the parent.

 

You are a genius my friend