In wave phenomena, the energy carried by a wave is proportional to the square of its amplitude. However, when comparing waves of different frequencies but the same amplitude, the energy carried per unit time, or power, can be different. This is because power is determined not only by the amplitude of the wave but also by its frequency.
The energy carried by a wave is directly related to the number of oscillations or cycles it completes per unit time. In the case of a high frequency wave, it completes more cycles within a given time compared to a low frequency wave. Each cycle represents a transfer of energy, so a higher frequency wave transfers more energy per unit time than a lower frequency wave.
To illustrate this, let's consider two waves—one with a high frequency and the other with a low frequency. Since both waves have the same amplitude, they have the same maximum displacement from the equilibrium position. However, due to the higher frequency, the high frequency wave completes more cycles in the same time period compared to the low frequency wave.
Each cycle of the high frequency wave transfers energy, and since there are more cycles per unit time, the total energy transferred per unit time (power) is greater. In contrast, the low frequency wave completes fewer cycles per unit time, resulting in a lower total energy transfer per unit time.
Therefore, even with the same amplitude, a high frequency wave carries more energy than a low frequency wave because it completes more cycles and transfers energy more frequently within a given time period.