Do you have an aftermarket amplifier or radio, or factory-installed components only?

These audio interference problems can be elusive. Here is a test to isolate the cause:

Remove the fog lamp fuse, so the relay operates but the lights do not. Is the "pop" still there?

If Yes, add a diode across the relay coil. Any sort of rectifier diode, like a 1N2071, will do. Cathode (the end of the diode with a stripe) connects to the relay pin that went to the blue/yellow wire at the headlight switch. It is more effective to mount the diode at the relay then under the instrument panel.

Advise results. If this helps, but does not eliminate the problem completely, a "snubber" (resistor and capacitor in series) will be next.