[chris (OP)]

My apartment is very close to a busy road. Can the equivalent of noise-cancelling headphones be made for my flat to keep the noise down?

What do you think?

[alancalverd]

Not a problem in principle but you can buy such good active noise reduction (ANR) headphones that it is hardly worth making your own. Sennheiser and Bose are favoured by aviators but in-ear ANR buds may be more socially acceptable than aircrew cans - though fashion changes!. 

[cinka]

That might help but keeping your window close, that might help too.

[glot]

Last century, white noise generators were sold to cover up random noises.