Do you mean car battery or rather something else?
A car battery or a power pack for, say, a cordless drill.
I also hear popping in my Logitech X-540 computer speakers (connected to the mains) when lights are turned off.
Unfortunately that does not really help. It could be radiated energy being picked up by the audio circuitry (even the leads to the loudspeakers) or it could be energy conducted via the mains wiring.
I also hear popping in battery-powered portable AM radio.
In that case, you have shown that there is significant radiated energy.
Perhaps the light switch is question has aged and its contacts do not abruptly open but have a small amount of bounce. Maybe a new light switch would solve the problem. Other than that, a series connected capacitor - resistor pair across the switch contacts -- as
JGO suggests -- would quench the arc.