If you are curious to see how this happens mathematically, the idea is that the density wave is proportional to \(−d\xi /dx\), and the reflected displacement wave goes like \(\xi_{refl} = −\xi_{inc}(−...If you are curious to see how this happens mathematically, the idea is that the density wave is proportional to \(−d\xi /dx\), and the reflected displacement wave goes like \(\xi_{refl} = −\xi_{inc}(−x)\), where the first minus sign gives the vertical flip and the second the horizontal one.
