Final answer:
The energy of a wave does not directly increase with an increase in wave speed; it depends on the wave's amplitude. For longitudinal waves, as speed increases, the wavelength increases but the period stays the same. Energy and wave nature observation is linked to amplitude changes, not speed.
Step-by-step explanation:
When considering whether the energy of a wave would increase or decrease if the speed of the wave increases, it is important to know that the energy carried by a wave is not directly determined by its speed. Instead, the energy of a wave is primarily dependent on its amplitude. Therefore, if the speed of the wave increases but the amplitude remains constant, the energy of the wave does not change simply because of the increased speed. The energy would only increase if the amplitude were to increase.
However, in some scenarios, an increase in speed can be accompanied by other changes. For instance, a longitudinal wave traveling into a medium in which its speed increases will experience changes in its wavelength and period; the wavelength will increase but the period will stay the same. This is because the frequency of a wave is defined as the number of cycles per second, and if the wave is moving faster through the medium without changing frequency, the peaks of the wave must be farther apart, thus increasing the wavelength.
Similarly, the wave nature of matter becomes easier to observe as the energy increases, but this concept relates to the quantum mechanical nature of particles, not the standard wave mechanics in a medium. Lastly, the speed of propagation in a medium is usually constant, and as the frequency changes, the wavelength changes as well to ensure the speed remains the same in accordance with the wave equation v = f × λ (where v is speed, f is frequency, and λ is wavelength).