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Inspired by Barnard 68, a Bok globule, that undergoes stable oscillations, weperform multi-phase hydrodynamic simulations to analyze the stability of Bokglobules. We show that a high-density soft molecular core, with an adiabaticindex $\gamma$ = 0.7 embedded in a warm isothermal diffuse gas, must have asmall density gradient to retain the stability. Despite being stable, themolecular core can still collapse spontaneously as it will relax to develop asufficiently large density gradient after tens of oscillations, or a few $10^7$years. However, during its relaxation, the core may abruptly collapse triggeredby the impingement of small-amplitude, long-wavelength ($\sim$ 6 $-$ 36 pc)sound waves in the warm gas. This triggered collapse mechanism is similar to asonoluminescence phenomenon, where underwater ultrasounds can drive air bubblecoalescence. The collapse configuration is found to be different from bothinside-out and outside-in models of low-mass star formation; nonetheless themass flux is close to the prediction of the inside-out model. The condition andthe efficiency for this core collapse mechanism are identified. Generallyspeaking, a broad-band resonance condition must be met, where the coreoscillation frequency and the wave frequency should match each other within afactor of several. A consequence of our findings predicts the possibility ofpropagating low-mass star formation, for which collapse of cores, within a massrange short of one order of magnitude, takes place sequentially tracing thewave front across a region of few tens of pc over $10^7$ years.

Sound-Triggered Collapse of Stably Oscillating Low-Mass Cores in a Two-Phase Interstellar Medium