The snare drum works by hitting the top or batter head, which then causes the bottom head and snares to vibrate, giving the typical snare drum sound. The snares will therefore vibrate when any drum near them is also struck.
If you are getting any other overtones, like high-pitched whines or similar, then your drum needs tuning and/or dampening. Any other low-pitched instrument e.g., the bass - will also cause snares to vibrate in sympathy. The only snare drum to not vibrate like this is an electronic one.
Keith, June 2009