Buy a better power adapter! Normally, when running on batteries, you're using low voltage, DC (direct current) power, usually 6 ~ 9 VDC. Your house electrical power is higher voltage, 115~120 VAC. Your AC adapter lowers your house voltage from 120VAC, to the required lower voltage, and converts the alternating current, AC, to direct current, DC. If the AC adapter is of a poor design, it does not properly filter out the AC, and induced the buzz you're hearing. This is caused by your house electricity alternating polarity 60 times per second.