It is easy to observe the wave motion in a string but it doesn´t tell the whole story of wave properties. A string wave can't diffract or refract.
Sometimes simple explanations cause misunderstandings. Here a string wave is polarised by a narrow slit. Light, however, is polarised by a special Polaroid filter and not a slit.
Wave speed in a string
The velocity of a wave in a string is related to the tension and mass per unit length of the string:
Different guitar strings have different diameters and so different values of μ, mass per unit length. Therefore, the speed in each string will be different and they will vibrate with different frequencies.
Use quizzes to practise application of theory.