spaceship - Old SF story about the need to destroy an out-of-control passenger ship with a nuke before it crashes?

I'm trying to pin down a memory of a short story which I first read sometime in the early-to-mid 1980s (in an anthology I found in a school library, I think). I later found it again in another book, in another library, sometime in the 1990s. I remember the general plot, but not who wrote it. I have the impression that the story was already pretty old before I first ran across it.

Here's the plot outline:

1. 
   

   As the story begins, a spaceship containing hundreds (or even more?) of passengers is returning to Earth from some other planet.

   
   



2. 
   

   Something goes terribly wrong, and they lose the main engine. (Which may have been the only engine -- I'm not sure of the technical details.) I don't recall if it was accident, sabotage, a meteor strike, or what, but their main means of propulsion is gone, with no hope of fixing it any time soon.

   
   


3. 
   

   The timing is terrible. The ship is still on a trajectory that has it approaching Earth at high speed, and it badly needs to decelerate if there's to be any hope of touching down safely instead of slamming into the planet so hard that it will inevitably kill everyone aboard. But now the ship can't decelerate (nor change course to miss Earth entirely, which could have bought them valuable time), and there's only a matter of some hours left before the projected time of impact.

   
   


4. 
   

   Some political and military leaders meet on Earth for an emergency conference to discuss their options. What it comes down to is that a) there is no way to save the passengers and crew of the ship, no matter what they do, but b) if they do nothing at all, this will also mean the tragic deaths of millions of other civilians in the region which the ship will crash into. Not so much because of the shock of impact, but because of the sound in the minute or so before that.

   
   


5. 
   
   

   My memory gets blurred on the physical details of what makes the sound so bad . . . but I think the general idea may have been that such a huge metallic mass, moving so incredibly fast as it comes down toward the Eastern Seaboard of North America (or perhaps some other densely populated bit of the globe?), will be "screaming" in such a way that the vibrations racing through the air will shatter zillions of pieces of glass and/or otherwise cause huge numbers of fatalities down on the ground, even before the ship strikes whatever bit of the Earth's surface it is projected to strike.

   
   


6. 
   

   The final decision is that the lesser of two evils is to send up a missile (nuclear warhead, I think?) to vaporize the ship before it comes plummeting through the air near an urban area.

   
   


7. 
   

   I think that the officers aboard the ship either already knew, or very strongly suspected, that everyone aboard was doomed after the main engine had dropped dead. But the Captain and his loyal subordinates do their best to maintain a stiff upper lip in order to prevent mass hysteria from breaking out among the passengers. There's one bit where it is announced that a rescue ship is coming up from Earth to pull alongside the falling ship and then they'll transfer the passengers to safety. I believe the Captain knows darn well that the laws of physics do not make such a maneuver possible at this late date, and thus "a rescue mission" cannot be the intended function of the fast-moving blip on the radar screen that is headed straight for his ship, but he sees nothing to be gained by telling everyone the truth. So most of them die in blissful ignorance.

   
   

Answer

It's the novelette "Sound Decision" by Robert Silverberg and Randall Garrett. You can read it here. It was adapted to radio (drastically abridged) as an episode of Exploring Tomorrow which you can listen to here.

Here are some excerpts to show how the story fits your description.

The spaceship is coming in from Mars:

The Martian Queen was a luxury liner of some five hundred metric tons, belonging to Barr Spaceways. She was, at the time, making a "short-run” orbit from Mars to Earth, carrying a hundred and fifty passengers and a crew of thirty, including stewards.

The cause of the mishap is unknown:

Just exactly what went wrong with the drivers isn't known or knowable; the four men who might have known were dead within seconds after it happened. There are several things that could have caused the disaster—an accident which, except for the level-thinking of one man, might have caused the deaths of many more than the mere handful who died in a sudden blaze of light.

The passengers are told a comforting lie which is literally true:

"Your attention please! Your attention please! The ship is falling out of control, but there is absolutely no danger of our hitting Earth. A rocket from the spaceport will be here in two minutes. Repeat: a rocket from the spaceport will be here in two minutes. Please wait quietly, and be ready for it when it comes.”

The danger to people on the ground is from the shock wave:

"But its actual impact with Earth’s surface isn't going to be the thing that will do the damage. It won’t matter whether it comes down in Long Island Sound or in Times Square—it’s the impact with the atmosphere that will cause about twenty million deaths.”

No one said anything. The five men in the screen looked at him in blank-faced horror.

"You know what happens when a jet plane goes over a city too low?" Stanley said. "A supersonic jet can break windows. What sort of sound wave do you think a five-hundred-metric-ton spaceship will cause at—seventy-two thousand miles an hour?

"I’ll tell you. It would flatten every structure for miles around. If that ship hits Long Island Sound, New York City will be toppling in ruins before it ever arrives! Every town on Long Island is going to be pancaked. From Newark, New Jersey, to Hartford, Connecticut, that shock wave will knock over everything standing. This isn’t a matter of a few people in a ship dying; it's a matter of millions!”

The spaceship is nuked:

"Oh, it won’t land,” said Stanley. His voice sounded old and tired. "There won’t be any crash. I sent up an XV-19 under robot control several minutes before you gentlemen got together. It was loaded with a thermo nuclear warhead. Captain Deering will—or I should say has—guided it in. The Martian Queen was vaporized over a minute ago. It was the only thing to do.”