Where is energy being applied to the system?
what part of the wave does an increase in energy affect?

Well i cant answer the first question due to absence of diagram
For the second queation, the energy affects the Frequency of wave, the higher the ebrgy the higher the frequency. Since frequency =1/Period,energy can also be said to alter the period. Since wave speed = Frequency *Wavelength, the speed is also increase due to increase in the frequency.
its amplitude increases too by the way.

This is what a calorimeter is used for simpler ex, to measure calories in food.

The object's initial distance above the groundthe object's initial velocity