Do Waves have mass? Do any form of electromagnetic waves like visible light have mass? It is known that all electromagnetic waves have energy. According to Einstein's
$$ E^2=p^2c^2 + m^2c^4 $$
formula, the energy of a particle like photon, which shows wave properties as well, is derived from its mass and momentum. Some suggest that photons are indeed mass-less and that photons have energy due to there momentum, but momentum itself is equal to mass times velocity, $p=mv$.Then how can a body have momentum and not mass? The experiment on photoelectric effect by Einstein clearly proves Planck's theory of energy packets(photons) as correct, thus providing concrete evidence for the wave-particle duality of photons. Could anyone provide an explanation that is understandable to interested high-school students? Thank you:)
 A: You want a high school level answer.  I will try.
There are fundamental definitions established at the creation of the universe.  Physicists have deduced many of these fundamental quantities, which define relationships between things like matter, energy and even time.  One fundamental definition is the invariant speed of light, and the fact that by definition mass can't travel at the speed of light.  However, observed effects of light require more.  Light demonstrates the properties of a particle; it can't just be a 'wave'.  Hence the photon, which carries specific packets (quanta) of energy and reacts like a particle.  Another requirement of known physics is that photons have zero rest mass; they only exist at the speed of light.  Photons are very special 'particles'.  Photons are better thought of as a description defined by observation and theory.  Formulas such as those you quote are simplified for use.  For a full understanding, if that is even possible yet, you must move into quantum physics, which even Dr. Richard Feynman admits is rather weird.  It's certainly a bit beyond high school, though you may want to refer students to Feynman's lecture series available on YouTube.  
