When two waves have the same frequency but different amplitudes, the primary difference lies in the magnitude of their displacements or intensities.
Amplitude: The amplitude of a wave represents the maximum displacement or magnitude of the oscillation from its equilibrium position. In the context of a wave's amplitude, a larger amplitude corresponds to a greater maximum displacement or intensity of the wave. So, when comparing two waves with the same frequency but different amplitudes, the wave with the larger amplitude will exhibit more significant oscillations or a greater intensity compared to the wave with the smaller amplitude.
Energy: The amplitude of a wave is directly related to its energy. Higher amplitude waves carry more energy compared to waves with smaller amplitudes. Therefore, a wave with a larger amplitude will generally have a higher energy content than a wave with a smaller amplitude, assuming all other factors remain constant.
Perception: In the case of waves like sound or light waves, the amplitude affects the perception of the wave's intensity or loudness (in the case of sound) and brightness (in the case of light). A higher amplitude wave will be perceived as louder or brighter than a wave with a smaller amplitude, given the same frequency.
To summarize, the difference between two waves with the same frequency but different amplitudes lies in the magnitude of their displacements or intensities. The wave with the larger amplitude will have greater oscillations, carry more energy, and be perceived as more intense or significant compared to the wave with the smaller amplitude.