<p>The accelerated motion of celestial bodies like black holes and Neutron stars generate gravitational waves. These waves propagate in universe with the speed of light and carry energy and momentum from their sources. They have been detected from a range of astrophysical sources, including binary star systems, black holes, and neutron stars. This abstract highlights both theoretical and observational aspects of gravitational wave sources, with a particular focus on cylindrically symmetric sources. Cylindrically symmetric spacetimes offer a simplified yet effective framework for exploring gravitational wave generation and propagation. The main fucus here is incorporating a time conformal factor in the cylindrically symmetric spacetime by using the Noether symmetry equations. These models capture the dynamical nature of cylindrically symmetric spacetime and facilitate the derivation of conservation laws corresponding to both exact and approximate Noether symmetries. This technique provides a clearer understanding of the transfer of energy and momentum during the emission of gravitational waves. The real astrophysical sources often have more complex geometries, the time conformal cylindrically symmetric models provide valuable insights into the fundamental properties and behavior of gravitational waves, enhancing our understanding of gravitational wave physics and supporting advancements in theoretical and observational techniques.</p>