The company building Elon Musk's 740mph train just filed for a building permit in California

The company developing Elon Musk's Hyperloop idea claims passengers could be travelling at close to the speed of sound within the next three years, having just filed for a building permit in California.

The Hyperloop concept involves firing a train full of people through a low-pressure tube at speeds of up to 740 mph. It has been described by Musk as a mix between Concorde, a rail gun, and an air hockey table. It could take you from Los Angeles to San Francisco in under 30 minutes.

Hyperloop Transportation Technologies, the company taking the lead on turning Hyperloop into a reality, told CNBC that it has filed for a construction permit to build a five mile track in Quay Valley, California.

"We are announcing the filing of the first building permit to Kings County to the building of the first full-scale hyperloop, not a test track," Bibop Gresta, the COO of Hyperloop Transportation Technologies, said during an interview at Davos on Thursday.

Construction is set to begin in the second quarter of 2016 and Hyperloop could open in 2018 to the public.

"In 36 months we will have the first passenger in the first full-scale hyperloop," said Gresta.

The company is reportedly looking at where it will place its pylons and carrying out a number of soil tests.

Gresta told Business Insider last October that if the California prototype is successful, larger versions of Hyperloop could be built across the world. Indonesia, Saudi Arabia, Botswana, and India are all in contention. "We think the first Hyperloop will be built in a country where there's a lack of infrastructure and less regulation," he said in an interview where he claimed Los Angeles was a better innovator than Silicon Valley.

Hyperloop Transportation Technologies is being led by CEO Dirk Ahlborn and a group of over 100 scientists and engineers. Musk has previously said he would take the idea forward himself if he wasn't so busy leading other companies like Tesla.