In the context of waves, such as liquid waves or air waves, increasing the amplitude does not directly result in an increase in momentum or speed of the wave itself. The momentum and speed of a wave are determined by the properties of the medium through which the wave is propagating, rather than the amplitude of the wave.
The amplitude of a wave refers to the maximum displacement of particles in the medium from their equilibrium position when the wave passes through. For example, in a water wave, the amplitude is the height of the wave crest or the depth of the wave trough from the undisturbed water level. In an air wave (sound wave), the amplitude refers to the maximum compression or rarefaction of air particles.
When the amplitude of a wave increases, it means that the wave becomes more intense or carries more energy. However, this increased energy does not change the momentum or speed of the wave itself. The wave's speed depends solely on the properties of the medium through which it travels, such as its density and elasticity. In general, waves with larger amplitudes can transfer more energy to the medium they are passing through, but their speed remains constant in that medium.
It's important to note that there is a distinction between the speed of a wave and the speed of individual particles within the wave. In some cases, the speed of particles within a wave may vary with the wave's amplitude. For example, in a water wave, the water particles move in circular orbits as the wave passes through, and the size of these orbits can be influenced by the wave's amplitude. However, this does not change the overall speed of the wave itself.