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Acoustic wave can destabilize the flame and has a potential in firefighting, but the influences of the sound source and its frequency are still poorly understood. This work applies a loudspeaker to extinguish a laminar diffusion propane flame of 5–25 mm high, where the local sound frequency is 50–70 Hz and sound pressure is 0.8–3.2 Pa (92.0–104.1 dB). Results reveal a constant flame pulsating displacement at the extinction limit, independent of the sound environment used. Such a flame pulsating displacement is found to be caused by the motion of the speaker membrane (or diaphragm) and its induced wind, which could be two orders of magnitude larger than the displacement of the air that transmits acoustic wave. Thus, under the influence of sound source, a critical flame strain rate, stretched by the pulsating airflow, can be formulated to characterize the blow-off limit better than the local sound pressure. The sound source with a lower frequency can produce larger pulsating displacements of both membrane and flame, and thus promoting extinction. This work improves the understanding of flame dynamics under the external sound field and source, and it helps establish a scientific framework for acoustic-based fire suppression technologies.