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I don't understand how these two quantities (amplitude + wavelenght) are not directly related to each other.
If my understanding is correct amplitude is displacement thus distance, same as wavelength.
What happens if you keep increasing the amplitude to the point where displacement becomes greater than a wavelenght?
As I understand it, the amplitude of a sound wave is the particle's displacement from its equilibrium state (at rest).
The wavelength is the distance between points of the same phase or the distance over which the sound repeats. If it repeats only once, then the wavelength is the distance it takes for a complete cycle of rarefaction and compression.
So, amplitude and wavelength are both measures of distance, however, they're measured in directions generally perpendicular to one another.
If you pop a balloon and generate a sound wave, a given air particle may change it's position first in the direction of the wave (compression) and then in the opposite direction (rarefaction). The distance it travels in one direction is the amplitude. If the wavelength is small, then this cycle will occur quickly. In fact, $c = \lambda f$, the velocity of the sound wave is a product of the wavelength and the frequency.
