Recently, a new method, called the extended sampling method (ESM), was proposed for the inverse scattering problems. Similar to\nthe classical linear sampling method (LSM), the ESM is simple to implement and fast. Compared to the LSM which uses fullaperture\nscattering data, the ESM only uses the scattering data of one incident wave. In this paper, we generalize the ESM for the\ninverse acoustic source problems. We show that the indicator function of ESM, which is defined using the approximated solutions\nof some linear ill-posed integral equations, is small when the support of the source is contained in the sampling disc and is large\nwhen the source is outside. This behavior is similar to the ESM for the inverse scattering problem. Numerical examples are\npresented to show the effectiveness of the method.
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