[C. C. Rider]

I think the sound the OP is hearing is caused by the fill valve which may need cleaned or replaced. The fill valve is kicking on when other water is being used due to the drop in water pressure in the line when the other water using appliance kicks on.

If the fill valve is kicking on at odd times without water being used elsewhere, it may be due to a leaky flapper which can be replaced easily.

Sometimes the fill valve gets a little dirt in it. This can be cleared out by first turning off the water supply to the toilet. Then press down and turn counterclockwise on the top of the valve about 1/4 turn. The valve cover will lift off.

Then, while holding a drinking glass (or similar) over the top of the fill valve, turn the water supply back on. This will blow water out of the top of the valve and the glass will deflect it back into the tank.

After 10-15 seconds of this cleaning out, turn the toilet water supply off again. Then replace the top of the valve by pressing it down and turning it clockwise about 1/4 turn. Then turn the water supply back on and do a function check.