The acoustic field of a turbulent lean cpremixed open flame is numerically investigated by a hybrid method solving the Navier-Stokes equations in a large-eddy simulation formulation and the acoustic perturbation equations. The interaction of acoustic modes of a burner plenum and the turbulent flame is analyzed with respect to the sound emission of the flame. It is investigated if a simplified computation yields a good broadband agreement of the sound pressure spectrum with experimental measurements. The results of two numerical setups, i.e., the first configuration consists of the burner plus the plenum geometry while in the second configuration the plenum is neglected, which is often done in technical applications due to computational efficiency reasons, are compared with experimental findings. It can be concluded that the plenum has a pronounced impact on the dynamics and combustion noise of the open flame. To be more precise, the comparative juxtaposition of the numerical and experimental results shows a good agreement only for the full burner-plenum computation since the interaction of the acoustic quarter-wave modes of the burner plenum with the jet flow has to be captured. The interaction of these quarter-wave modes with the flow is analyzed and the acoustic response to heat release fluctuations of the flame of the full burner-plenum computation is compared to that of the simplified burner computation, in which the plenum acoustics is neglected. Due to the excitation by the plenum acoustics, the jet flow of the full burner plenum contains higher turbulent kinetic energy and the flame is excited at several additional frequencies which result in distinct peaks in the acoustic spectrum and a higher overall sound pressure level.