  Self-sustained oscillations arising from the interactions between the
hydrodynamic and the acoustic field are disastrous in engineering systems such
as segmented solid rocket motors and large gas pipelines. These self-sustained
oscillations (limit cycle oscillations) are also referred to as aeroacoustic
instabilities, which can be heard as a whistle. Understanding the change in
dynamical state by altering the control parameter in an aeroacoustic system is
critical in designing control strategies for aeroacoustic instabilities. In
this study, as the control parameter Reynolds number ($Re$) is varied, we hear
a change in the whistling frequency. We show that this change in frequency
occurs via the state of intermittency, which has bursts of periodic
fluctuations amidst the regime of the aperiodic fluctuations in acoustic
pressure fluctuations. At a higher Reynolds number, we observe an abrupt
transition from one limit cycle oscillation (LCO) to another limit cycle
oscillation during the shift in whistling frequency. Further, we use
synchronisation theory to investigate the coupled behaviour of the acoustic and
the hydrodynamic fields. The acoustic pressure ($p'$) and hydrodynamic ($v'$)
fluctuations during LCO exhibit phase synchronisation. Thus, we conclude that
the shift in whistling frequency is a transition between the two phase
synchronised limit cycle oscillations that occurs either through the state of
intermittency or abruptly. The periodic bursts of intermittency correspond to
the phase-synchronised periodic $p'$ and $v'$, and the aperiodic epochs
correspond to the desynchronised aperiodic $p'$ and $v'$.
