Sign convention for backward traveling waves

In the December 2018 issue, Perkins and Ruiz¹ point out that if a 1D rightward traveling wave is written as A sin(kx – ωt), then a leftward traveling wave should be written as A sin(–kx – ωt) and not as A sin(kx + ωt). Use of the correct expression is crucial in deriving the Fresnel equations for the reflection and transmission coefficients of a wave incident on an interface, such as when a wave encounters a knot joining a string of one linear mass density to another.² Thus it is important to convince students of the correct leftward expression. Perkins and Ruiz explain it by saying the sign of the wave vector k should be switched. That is a good argument for students who have been exposed to the modern physics idea that the momentum vector of a 1D wave is ħk...