Question

Which statement best describes a wave?

the repetitive disturbance of particles within a medium.

a disturbance between particles in a material.

the energy contained in the particles of a medium.

a continuous transmission of energy from one location to the next.

Answer 1

Yuck. All of these are flawed. The key aspect of a wave, what makes a wave a wave, is that it is a collective excitation of the particles in a medium. That is, you can only describe it by considering what EVERY particle in the medium is doing. It's like the difference between your score on a test and class average. Class average is by definition a phenomenon defined on the entire class. You cannot speak of the "class average" of just one student, or even two. In the same way, you cannot speak of a wave involving one particle -- by definition it is a phenomenon defined on all the particles.

But...aside from that, there are few other restrictions on a wave. It need not be repetitive, it can be a one-shot pulse. It's not synonymous with the energy of the particles: they may have energy unrelated to the wave disturbance. It need not transmit net energy from one place to another (for example a "standing" wave does not), and even if does, it need not be continuous, since the wave itself need not be continuous.

I'd say the least bad choice is the first, because it clearly refers to something that happens to ALL the particles, which is key. The minor error of thinking it is a repetitive disturbance is perhaps a result of the fact that we often study the simplest possible waves, which are the "normal modes" of the medium, and which indeed are simply repetitive -- have a definite frequency. It may be whoever wrote the question is focussed so much on these waves he has forgotten that there are many others. That is, perhaps he is so focussed on the regular waves that you see crashing on a beach that he has forgotten about things like tidal waves, or "rogue waves," things that aren't repetitive.

Answer 2

the energy contained in the particles of a medium.