There are two main techniques used to adjust the frequency of an AWG (or any function generator that uses digital methods to create signals). The most common is DDS, and the second is easier to understand, which is a variable clock.
This circuit uses a variable clock (green waveform) to control the frequency of the output (blue waveform, which I've programmed with the logic buttons to emulate a capacitor charge curve). It is located to the left of the D-Type flip-flops ring counter. Try changing it from 2ms to 1ms. This will double the frequency. The reason is that the clock accesses one point in memory at a time. So the faster it cycles through each sample, the higher the frequency.
DDS is a clever way to adjust the frequency of the output without changing the sample rate or clock frequency. DDS calculates the next phase angle based on the desired frequency and uses that to pick which point in memory to access next (skipping some to speed up, if necessary). The circuit is more complicated than just a variable clock. Maybe I'll have a try at DDS next...
My other AWG circuits if you'd like more info.
Basics https://everycircuit.com/circuit/6641355690082304
Upgraded https://everycircuit.com/circuit/6141640988950528
DDS https://everycircuit.com/circuit/6214446053326848
NCO: https://everycircuit.com/circuit/5760185112723456
