When a wave transitions from one string to another with different linear densities, its frequency remains constant, while the wavelength changes. The change in wavelength occurs due to the differing speeds of the wave in each string, which is influenced by the linear density. If the wave is traveling through two connected strings, the frequency at the boundary remains the same as the incoming wave. However, the wave speed will differ, resulting in a longer or shorter wavelength in the second string. Understanding these relationships is crucial for analyzing wave behavior across different media.