Show me the Money

So up until now, we've focussed on the anatomical factors behind our vocal cords and touched on the physics backing up sound; however it's all been rather qualitative information. What we need now are numbers! Well, there's this incredibly helpful tool called pitch to frequency mappings! They provide pitch in relation to Hertz, a radical visual to help one conceptualize such measurements.

(picture from http://www2.siba.fi/akustiikka/index.php?id=45&la=en)

​Now you might be thinking, "Well that's fine and dandy, but I want to know how much force from me personally is required to match such frequencies? What about energy?" Well, the answer to those questions really aren't so simple. First of all, Hertz is a measure of vibrations while force and energy are not, so some kind of third party rule or equation is going to be necessary to carry of such a conversion. Liklier than not, such a third party is going to be complex. Second, the way our bodies are designed is going to affect how much force/energy is necessary to aquire a certain pitch. For instance, men have a much lower vocal range than women because their voice boxes are often larger. This means that the force and energy required for a man to achieve high notes is going to differ greatly compared to a woman. And if that weren't complex enough for you, there are even more factors that play into pitch acheived by vocal cords like elasticity and acid reflux. To conclude, calculating the numerical value of energy and force required to achieve pitch is a complex process dependent on the individual vocalist. Unfortunately it isn't entriely reasonable to make such calculations under casual circumstances.