For a wave on a 1d string that hits a boundary between 2 strings of different material we get,

˜f(z<0)=˜AIei(k1)zωt+˜ARei(k1zωt) ˜f(z>0)=˜ATei(k2)zωt

where continuity (BCs) give,

˜AR=(k1k2k1+k2)˜AI ˜AT=(2k1k1+k2)˜AI

Is the transmitted wave in phase with the incident wave?

A) Yes, always B) No, never C) Depends

For a wave on a 1d string that hits a boundary between 2 strings of different material we get, ˜f(z<0)=˜AIei(k1)zωt+˜ARei(k1zωt) ˜f(z>0)=˜ATei(k2)zωt where continuity (BCs) give, ˜AR=(k1k2k1+k2)˜AI ˜AT=(2k1k1+k2)˜AI Is the transmitted wave in phase with the incident wave? A) Yes, always B) No, never C) Depends Correct answer: A