The question is that: How could you make a Wien bridge tune to different frequencies?
Since the frequency is depended on the value of the resistor and capacitor we should use a variable resistor and capacitor. But, I am not sure if this is the right approach.
For a single frequency Wien Osc. you need 2 resistors (of the same value) and 2 caps (of the same value). To vary the frequency over a large range you require a dual gang pot for the resistors so that you can vary their values together. Then have say 4 frequency bands. Each band would be selected by switching in a pair of same value capacitors. 8 capacitors in all. This avoids the difficulty of trying to implement a dual gang capacitor.
Here's one I designed a while ago.
Here is the block diagram of the iconic HP 204C oscillator:
As you can see, it uses a ganged air variable capacitor as the primary tuning elements.
A pot is used to adjust the amplitude as controlled by the AGC (automatic gain control).
The complete schematic is in the manual which can be downloaded. It uses BJTs and JFETs exclusively (no ICs at all).
Incidentally, my 204D, made approximately 50 years ago, still works fine.
decades ago, in university, I built a 100:1 tuning-range Wein using cadmium cells from Edmunton Scientific. In a pack of 10, I found at least 2 that tracked (as light varied from a 28 volt bulb) rather well. To handle mistracking, another cell + another bulb was used to adjust the nominal_3:1 feedback gain.
