This paper introduces the extensive application of Bessel functions, a core topic in mathematical physics courses, at the forefront of research in gravitational wave physics. We focus on the significance of Bessel functions through a detailed discussion using the example of gravitational wave radiation from cosmic strings.  Additionally, we briefly outline their application in higher-order mode gravitational wave radiation from binary systems and gravitational waves from phase transitions. This study can serve as an example of educational reform integrating undergraduate core curriculum teaching with undergraduate research.