I am using an AC Power supply, and the frequency of the wall plugs is around 50hz. Is there a way to increase this frequency keeping everything the same?
There are 2 ways of doing it: the hard way, and the hard way.
Connect an AC motor for the input frequency to a generator of the output frequency.
Rectify the input, then use a function generator of sorts with an H bridge.
A rectifier followed by an inverter.
It's easier said than done, especially if you need a pure sine wave, or if you need large quantities of power at specific frequecies. As with all engineering, you design for cost and performance - if a mod square wave inverter will do the job, use that. If all you need is a few milliamps, maybe a square wave and a filter will do the trick. If you need megawatts, than you might very well consider something called a motor generator - literally, an electric motor driving a generator that has the desired output.
Because a pure 60 Hz sine wave does not contain any other frequency, there's no passive way to do this - you just have to make what you need.
An alternative is a motor, a variable speed gearing system, and a generator. This was used before semiconductor technology advanced to the point that variable frequency drive (VFD) inverters became practical. It still works, and if you happen to have all the components handy it's still a viable alternative, but VFD would usually be a better choice.
I work on high end Ups's and it is basically the principle on how they work. In layman's terms, Incoming a/c is converted to d/c by Thyristors or Scr's firing on the rectifier which is then stored in a capacitor bank. To convert dc back to a/c the units I work on utilize IGBT's for the fast switching to create the alternating waveform at the frequency desired. All the switching is microprocessor controlled and can be manipulated to change the outgoing ac to your desired frequency level. Although as mentioned before your waveform at this point resembles a square wave. In order to generate a sinewave it is then ran through transformers,. Etc which will eventually round the squarewave into a nice clean sinewave
It's called a Variable Frequency Drive.
It consists simply of a rectifier, which produces DC from the incoming AC, and an inverter, which produces AC from the DC.
The inverter usually works by producing a simple square wave of voltage, at several kHz, with the duty cycle or pulse width adjusted at the ~50 Hz frequency to give the desired current waveform in the motor.
A VFD will usually have some other logic, to adjust the voltage and current magnitude to suit the frequency, to apply reasonable torque to the motor, to control its speed, etc. This might not be the behaviour you want.
So in general, the AC is created from scratch. There is no way of simply modifying the frequency of a voltage.