If the speaker had an intermittent connection, for example in the connection between the solid voice coil wire and the stranded tinsel lead, then the speaker could radiply turn on and off twice with each cycle. However, you may not hear this as a rapid on/off but could perceive this as noise just like you can't see a light bulb alternating without a strobe. And, it's possible that either the condition or the degree of audibility could change with amplitude. It might explain a slight buzz but it wouldn't explain white noise. So, this may be an issue upstream in the signal path.
Reverse the left and right speakers at the amplifier terminal. If it shifts to the opposite side then it's in the electronics. Next, use the same approach with the amplifier input RCAs. Keep moving backwards until you have isolated the true cause.