A theoretical model for the generation of thermo-acoustic waves from a heated point source in a free-space and a half-space is proposed, where the source is suspended over a substrate. By directly applying the analytical results of a point source to a thin line thermo-acoustic speaker, the acoustic pressure field generated by the periodically heated thin line can be derived using a mathematical integration technique. To further generalize the results from a thin line speaker to a thin line array, the acoustic pressure response generated by the line array speaker can also be implemented in both free- and half-spaces. In this work, the characteristics of pressure fields generated by the thin line array are investigated in detail. The established model is well validated by comparing with the existing experimental results. The present findings not only can be extended to investigate thermo-acoustic responses generated by arbitrary sources, and also it can provide important design guidelines for the manipulation and optimization of thin line array thermo-acoustic devices.
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