Despite its crucial importance in physics, there are not many studies focusing on student difficulties and teaching strategies related to the (1D) wave equation in the PER literature. In order to contribute to fill this gap, we conducted a study with university students which focused on specific aspects that are crucial for understanding this equation. Our results include not only key learning difficulties and potential teaching strategies to circumvent them, but they also suggest that students can search for a deeper understanding of physics equations when prompted to do so.