NEW YORK — The museum devoted to the story of Sept. 11 tells it in victims’ last voicemails, in photos of people falling from the twin towers, in the scream of sirens, in the dust-covered shoes of those who fled the skyscrapers’ collapse, in the wristwatch of one of the airline passengers who confronted the hijackers.

By turns chilling and heartbreaking, a place of both deathly silence and distressing sounds, the National September 11 Memorial Museum opens this week deep beneath ground zero, 12 1/2 years after the terrorist attacks.

The project was marked by construction problems, financial squabbles and disputes over the appropriate way to honor the nearly 3,000 people killed in New York, Washington and the Pennsylvania countryside.

Whatever the challenges in conceiving it, “you won’t walk out of this museum without a feeling that you understand humanity in a deeper way,” museum President Joe Daniels said Wednesday.

The privately operated museum — built along with the memorial plaza above for $700 million in donations and tax dollars — will be dedicated Thursday with a visit from President Barack Obama and will be open initially to victims’ families, survivors and first responders. It will open to the public May 21.