How to use wave texture with a variable (random) length

I am trying to create a material on a plane, where the entire plane would be of one color(green, lets say), with just a band of black stripes in between with variable/random length. Something like this (sorry for the poor drawing, hope it gets the idea across):

In blender, I have been able to achieve something like this:

The node setup is as follows:

I cannot figure out how to randomize the wave's length. As I am using the gradient texture as the factor for the mix node, randomizing the gradient texture's border should do the trick (just my thought), but not able to figure out how. Please help...Thanks..

The noise produces a value in range $$[0, +1]$$, but it can be multiplied by a Max Height different than 1 to increase or decrease the range of possible heights. Alternatively you can use pass the noise through a color ramp to control the heights. Then this value is divided by 2, because the next step is to measure if y coordinate is either above or below that value from the middle. Finally use Multiply as a logical AND, to control if the pixel belongs to a strip or not.