A rectangular cavity inside a two-dimensional sonic crystal was theoretically and experimentally characterized by examining its response to a cylindrical source emitting narrow-band filtered noise bursts with central frequencies ranging from 2 to 12 kHz. A broadband intensity resonance was observed for frequencies within the full band-gap region of the sonic crystal (5.5-6.5 kHz). Unlike ordinary resonances, this broadband resonance depends on the reflection properties of the sonic crystal forming the surrounding walls rather than on the geometry of the cavity.