The word best can be subjective and is dependent on how much money you want to spend and what you can practically do with the technology available.
You're current strategy of listening to white noise via headphones at a volume so that it masks the noise of construction is not a good strategy because the volume of noise emitted by your headphones could be damaging your hearing system and it could be causing you permanent hearing loss. You need a system that will protect you hearing.
Ear Plugs and Ear Muffs - Passive Noise Reduction
The first thing you could do is wear ear plugs or ear muffs. These will reduce noise but not eliminate it.
Some issues with ear plugs are:
- some people find them uncomfortable to wear for prolonged periods.
- people with ear drum damage or ear infections cannot use them.
- to be effective, the plugs must be inserted correctly, with most of
the plug inserted within the ear canal.
- for hygiene reasons, most ear plugs are disposable and should only be
worn once.
- ear plugs made of rubber and fitted to you ears by a professional auditory expert can be reused, but they must be washed very carefully between each time they are used.
- they muffle all sounds, including the sounds in the room were you
are, so they make conversations and listening to music or other
sounds difficult. This also applies to ear muffs.
Some issues with ear muffs are:
- each muff must completely cover each ear
- the muffs must be periodically cleaned, preferably with antibacterial
wipes, for hygiene reasons and to prevent ear infections.
- ear muffs can be uncomfortable to wear for prolonged periods, but
generally are more comfortable than ear plugs.
- the muffs must be worn so there is no air gap between the muff and
the ear or sides of the head.
- for slightly increased noise reduction, ear plugs can be worn while
using ear muffs.
Some people, such as underground miners in some countries, must wear either ear plugs or muffs, or both, for the entire 12 hour duration of their working shift. Because of this, it is possible to wear either ear plugs or muffs constantly while you are at home, but it would not be an ideal situation. While sleeping it is possible to sleep with ear plugs inserted in ones ears, but it would be very difficult to sleep with ear muffs on. Which would be a problem for people who work night shift and must sleep during the day.
Active Noise Reduction
Noise cancelling headphones could offer a solution, but they are best at cancelling constant noise that has a limited frequency range, such as that produced by vehicle engines. They work by producing a sound with the same frequency as the disturbing noise but out of phase so the two sounds cancel each other.
With noise cancelling headphones it would be best to use headphones that surround each ear. The issues that I listed for ear muffs also apply to noise reduction headphones.
It may be possible to purchase a noise reduction system that could be installed in a room, but such a system would at best reduce noise in that room.
Alterations to the House or Apartment
These options may be expensive and may or may not be practical in your situation.
- Seal and thicken the doors (replace the door with one made of dense
timber). Use a door sweep at the bottom of the door to disrupt the
gap between the base of the door and the floor.
- Seal the windows and cover the windows with heavy drapes. The drapes act as a sound insulator.
- Add mass to the walls. This can include retrofitting sound proofing
insulation, which would be very expensive to do or you can hang
drapes or carpets on the walls.
- Soundproof the ceiling and floor by installing sound proofing
insulation above the ceiling and below the floor.
- If possible erect a noise barrier between the source of the noise and
your dwelling.
