Hey, recently I started a project making an intervelometer for my dslr. I decided that I would use the external shutter release pin. Here's the diagram:
In this I have to bridge those wires automatically with an arduino. I know that I can use relay or other mechanical methods but I don't want it to be noisy. So could someone please help me with this.
The only method to do it independently from the curcuit is using a relay.
You also can use a transistor (mosfet) or optocoupler in some cases, but it depend on parameters of switched signal.
In that case, check if there is a ground pin on the audio-jack looking thing in the picture in the first post, and if so you should be able to use that as a common ground
If you don't want to get too deep into the electronics part however, and want to keep it as simple as possible, then what @jim-p put would be the best solution. Just make sure to check the current rating of the reed relay.
Finally - as already stated here by several experienced members - the solution depends on the electrical situation on the side which you want to switch. Without some (basic) knowledge in electronics and measurement with a volt- and amperemeter you might quickly "brick" something expensive ... The smell of boiling electronic parts or burning printed circuit board tracks is paving the way of experience ...
Potential free switches are the least risk but still any intervention does include risks. No risk, no pain (but also less fun) ...