Boundary Behavior of Waves and Polarization

At a boundary the frequency carries across unchanged, because the source keeps driving the boundary at its own rate, so the new medium sets the speed and the wavelength adjusts through $\lambda = v/f$. A pulse arriving at a boundary both reflects and transmits: the reflection is inverted when the far side is slower or the end is held fixed, and upright when the far side is faster or the end is free, while the transmitted pulse is never inverted. Polarization restricts the oscillation to a plane perpendicular to the travel direction, which only a transverse wave has, and in a stack of polarizers the first filter halves unpolarized light while every later one depends on the angle to the polarization now arriving.

Four errors dominate. Letting the frequency shift at a boundary while holding the wavelength fixed, which would recolour light entering glass and change the pitch of sound entering water. Flipping every reflected pulse upside down without asking what is on the far side, and forgetting to draw the transmitted pulse at all. Applying polarization to sound, which oscillates along its own direction of travel and has no plane to restrict. And handling a polarizer stack by halving at every filter or by subtracting angles, which gives a nonzero result for crossed filters or zero for parallel ones.