+1 ^
Possibly the battery doesn't have enough charge. When the solenoid engages, the current goes way up and might have pulled so much current away from the solenoid coils it couldn't overcome the spring, and dropped the contact, which gives the battery enough grunt to pull the solenoid back in, which enageges the starter but there isn't enough current in the battery to run the starter and hold the solenoid in.
Round and round and round, dropping in and out. That'll make a buzzing sound.