The relationship between energy, wavelength, and amplitude in waves can be a bit complex, and it depends on the type of wave and the context in which it is being discussed. Let's examine the three cases you mentioned:
Tsunami Wave: In the case of tsunami waves, which are a type of water wave caused by underwater disturbances like earthquakes, the energy is primarily determined by the wave's amplitude rather than its wavelength. A larger amplitude means more water is displaced vertically, resulting in a higher-energy wave that can cause more significant damage when it reaches the shore. The wavelength, on the other hand, affects how the wave behaves as it travels across the ocean but doesn't significantly impact its overall energy content.
Sound Wave: In sound waves, which are mechanical waves that travel through a medium (like air or water), the energy is indeed related to the amplitude of the wave. When the amplitude of a sound wave increases, the pressure variations in the medium become more significant, resulting in a louder sound with more energy. However, the wavelength of a sound wave is related to its pitch, not its energy. As I mentioned in my previous response, pitch is determined by the frequency of the sound wave, and frequency and wavelength are inversely proportional for sound waves in a given medium. So, as the wavelength increases (and the frequency decreases), the pitch becomes lower, but the overall energy of the sound wave remains dependent on its amplitude.
Electromagnetic (EM) Wave: EM waves, such as light waves or radio waves, are a different type of wave that do not require a medium to travel through. The energy of an EM wave is indeed related to both its amplitude and wavelength. In the case of EM waves, increasing the wavelength generally means decreasing the frequency, as they are inversely proportional. As a result, EM waves with longer wavelengths have lower frequencies and lower energy. However, the energy carried by an EM wave also depends on its amplitude. Higher amplitude EM waves carry more energy, regardless of their wavelength. This is why, in the electromagnetic spectrum, gamma rays have the highest energy (short wavelength and high amplitude) while radio waves have the lowest energy (long wavelength and lower amplitude).
In summary, for tsunami waves, the energy is primarily affected by the amplitude, while for sound waves, it's primarily affected by the amplitude but pitch is determined by the frequency (and hence wavelength). In the case of electromagnetic waves, both the wavelength and amplitude play a role in determining the energy content of the wave.