Wind from kitchen sink drainage pipe
You don't have a trap seal, to prevent air from moving through the drain.



Only the dishwasher is draining through the trap, so there's no trap to prevent air from coming up the drain. you'll have to fix the plumbing, so that both the sink and dishwasher use the trap. 

Instead, the plumbing should look more like this...



Use a tailpiece like this, off the bottom of the sink.



This allows you to connect the dishwasher to the drain. You can trim the end of the tailpiece, so that it fits into the space you have.  

Connect one side of the trap to the end of the new tailpiece, and the other end to the drain pipe.

You'll also have to add a vent to the system. Depending on where you live, air admittance valves (AAV) can be used.



After looking more at the plumbing, you might not need additional fittings (other than for venting). 


Remove the sanitary tee connection from the drain.
Connect the dishwasher outlet to the sanitary tee, where it used to connect to the drain.
Connect the end of the trap (where the dishwasher used to connect), to the drain.


Basically, just swap these connections.