Why Does Wave Reflect at Impedance Discontinuity?

[decesicum]

Why does a wave reflect when it meets an impedance discontinuity? And why is there a 180 degrees phase shift of the reflected wave when the transmission line finished with short circuit and no phase shift when the far end of the line is opened?

 

[berkeman]

Tell us what you know so far about these questions, so that we can help you. We do not provide solutions to homework and coursework questions here on the PF (that's against our rules), but we are more than willing to help if you show us what your thoughts are so far.

Like, how do you define characteristic impedance? What is the relationship between the wave and the impedance of the medium that it is traveling through?

 

[decesicum]

The characteristic impedance of a cable (it was coaxial cable I was interested in) is, as far as i know, its high frequency impedance (if we supply the line with some signal, the line draws some current from the source and the ratio voltage/current defines the characteristic impedance of the cable. (the cable acts as a series of LC cells, and is lossy because of its resistance)
As regards the relation between wave and medium impedance, I don't know if there is a general formula to characterize this. I know that the wave's velocity depends on medium permitivity which in turn is dependendent on waves' frequency.