Energy Considerations in Waves

## Question:

From questions asked in our homework, I have some other questions:

Q1: In the SHM case, we have constant energy, p.e. + k.e. In the wave case, is it the total energy will also be constant? Even though it may not be a spring? Like if we use a string instead, with no elasticity?

How can we prove that if we are asked to in the exams? Do we have to prove different cases mathematically?

Q2: In the SHM case, we just have one medium only. But in the wave case, we have two, or even more mediums. What extra factors do we have to note in calculating the energy? Like from denser medium to less dense medium, the k.e. of a wave will change e.t.c? If the total energy is really constant, then will a wave traveling slower when entering a new medium gains some p.e.? Why does the extra energy come from?

Q3: I think waves do not necessarily be waves in shm pattern of movement. Then how come we can use the energy formular which is in the same format as a shm case?

Thanks!