Flow tones in a pipeline-cavity system are characterized in terms of unsteady pressure within the cavity and along the pipe. The reference case corresponds to equal lengths of pipe connected to the inlet and outlet ends of the cavity. Varying degrees of asymmetry of this pipe arrangement are investigated. The asymmetry is achieved by an extension of variable length, which is added to the pipe at the cavity outlet. An extension length as small as a few percent of the acoustic wavelength of the resonant mode can yield a substantial reduction in the pressure amplitude of the flow tone. This amplitude decrease occurs in a similar fashion within both the cavity and the pipe resonator, which indicates that it is a global phenomenon. Furthermore, the decrease of pressure amplitude is closely correlated with a decrease of the Q (quality)-factor of the predominant spectral component of pressure. At a sufficiently large value of extension length, however, the overall form of the pressure spectrum recovers to the form that exists at zero length of the extension.