DO NOT use a 9V battery to test a tweeter. And when testing a tweeter, keep one lead moving so it never sees DC, but gets a series of pulses that cause a scratching sound. Use only a 1.5V battery on tweeters and then, it's best only to test it in lieu of an ohm meter. 1.5V is also plenty to verify the polarity of a woofer.
9 volts across a tweeter is 10 watts, if the battery can supply the current. Many tweeters cannot tolerate 10 watts.