Is the extent of displacement a vibrating tuning fork related to resulting sound wave characteristic amplitude?

No, the extent of displacement of a vibrating tuning fork is not directly related to the resulting sound wave characteristic amplitude. The amplitude of a sound wave is determined by the strength of the vibrations and the medium through which the sound wave is traveling, while the extent of displacement of the tuning fork refers to the distance it moves from its equilibrium position during vibration. While the amplitude and displacement are related, they are not directly proportional, and other factors such as the frequency and wavelength of the sound wave also play a role in determining the overall sound characteristics.