Which is heavier sound waves or light waves ?

OK let's say we have a house made of bricks. The house represents sound waves and the bricks are the gas (air) molecules that make up the waves.

Now next door there is a house made of straw. The house represents light waves and the straw is the photons that make up the waves.

Clearly the brick house weighs a ton more than the straw house. And there's your answer, the sound waves are heavier. Why? Because the gas molecules are waaaaaaaaaay more heavy than photons.

And just tell the poor folks at Fukashima Japan that waves don't have mass. Nonsense.

Waves do not have mass. PARTICLES have mass. Light is both a wave and a particle so it does have mass according to Einstein.

Today it is viewed as massless because it has no rest mass.

So either light is heavier than sound or neither have any weight at all. Take your pick.

Light waves carry energy, and energy in some ways acts like mass (e.g., energy is what couples to gravity, really, not just matter), but at the level of quantum field theory, our best description, you have to talk about photons, and those do not have mass.

Photons are never at rest, and do not have rest mass.

Sound waves (photons don't have mass). Sound waves are pressure waves made up of the motion of molecules which do have mass, not sure how you would measure the mass though (perhaps the total displaced mass...)