Acoustic resonances are modified when objects are introduced into a chamber. The magnitude of these changes depends on the object position, size, and shape, as well as on its acoustic properties. Here, an experimental study concerning the resonant frequency shifts induced by a solid spherical object in a quasi-one-dimensional air-filled acoustic cavity is reported. It is shown that Leung's theory does not account quantitatively for the observations. A novel and simple approach is proposed, based on the wave equation in a cavity of variable cross section. The results fit more accurately the measured frequency shifts.