Final answer:
The higher-frequency wave has more energy compared to a lower-frequency wave of the same amplitude due to the square relationship with the frequency in mechanical waves, while in electromagnetic waves, energy depends on the photon quantity but is reflected by the energy of individual photons which is related to frequency.
Step-by-step explanation:
The statement that a higher-frequency wave has more energy than a lower-frequency wave with the same amplitude is referring to the fact that the energy of a wave is directly related to both its amplitude and its frequency. When we consider mechanical waves, the rate of energy transfer is proportional to the square of the amplitude and the square of the frequency. Therefore, if two waves have the same amplitude, the wave with the higher frequency will have more energy because it has a higher rate of energy transfer. This is highlighted in the equation for the energy of a photon in electromagnetic waves, E = hf, where h is Planck's constant and f is the frequency of the EM radiation. The energy transmitted by these waves does not depend on frequency but only on the amount of photons.
Moreover, in the context of the electromagnetic spectrum, higher-frequency electromagnetic waves such as X-rays have more energy and penetration power than lower-frequency waves like visible light. These high-frequency waves can carry more information and resolve smaller details when probing materials.