can someone explain why high frequency waves contain higher energy?
If these are EM waves we are talking about, then each photon has energy equal to hf where h is Planck's constant and f is the frequency of the wave. To say that high frequency waves "contain" higher energy is not quite correct. The energy of a wave is proportional to the square of the amplitude, which is related to the number of photons. So certainly it is correct to say that a photon of higher frequency has higher energy.
One intuitive answer:
All else being the same, it takes a stronger restoring force to produce a higher frequency oscillation - the easiest way to see this is to play around with the equation for a simple harmonic oscillator. A stronger restoring force means more energy is needed to produce the same displacement.
Another intuitive answer: The energy of a wave is in whatever pushes the peaks up and the troughs down. A higher frequency means more peaks and troughs, hence more energy.
Both of these answers are imprecise and hand-wavy descriptions of something that is clear and precise in the math.
thank you guys!
Separate names with a comma.