Animate an object along the z-axis in a sin wave So I wanted to make an animation of an object where it bobs up and down along the z-axis, like a sin wave on a graph. 

I understand one way of doing this with drivers, by which I add a driver to the z-axis of the object I want to move and then assign a scale, location or rotation to the empty driving the movement of the object (that was a bit convoluted I know, but it'll be better illustrated by the gif below). 

Is there a different method that I can use to achieve the same animation, but not require the use of a driver (something that I have to move or scale)? I want to be able to control the intensity of the waves through the use of some simple maths. For example: Sin(x) (the red line) and sin(5x) (the blue line) have a different frequency in waves.  

I want to be able to control the animation through using similar principles in Blender.
You can use the Graph Editor for this by adding Modifiers.

Simply add a single keyframe to your object's Z-Coordinate (right-click the property in the Property panel (N) and select 'Insert Single Keyframe') and then swap to the Graph Editor.

In the Modifiers properties panel add a Built-in Function, select 'Sine', and adjust the properties (Amplitude, Phase Multiplier, etc.).