Where the listeners stood
Three years ago this week, a capsule about as wide as a bicycle wheel fell out of the sky over the Great Basin carrying a cupful of asteroid. It came in at forty times the speed of sound and it was loud. Scientists had spread thirty-nine microphones across the desert to hear it, and a new paper uses those recordings to settle an old argument about sonic booms.
The argument is over one number. When something tears through the air at hypersonic speed, it leaves behind a cylinder of shocked gas, and the width of that cylinder decides the pitch of the boom you hear sixty kilometres away. Theory says the width follows from the energy dumped per metre, times a constant. Three famous derivations from the 1960s give three different constants, and the largest is 40% bigger than the smallest. The capsule makes a nearly perfect test object because it doesn’t melt or break up, and NASA knows its shape and its path. The paper measures the constant at every microphone, takes the median, and gets 0.396. The smallest of the three textbook values is 0.399. The largest, from a paper by Few, is ruled out.
I rebuilt the numbers from the public tables and got 0.403, which is close enough to trust the rest. Then I coloured the dots by which road each microphone was on, and the result changed.
The microphones were set out in three lines. Twenty of them, on the line called A, heard sound that left the capsule between 55 and 59 kilometres up. They give 0.39, right on the smallest textbook value. Ten more, on the line called C, heard sound from 44 kilometres, where the capsule had slowed to eight times the speed of sound. They give 0.66. That’s above Few, the value the paper rules out.
So the median isn’t a property of the boom. It’s a property of the survey. Line A has the most microphones, so Line A wins the vote. Give each road one vote and the answer is 0.48. Resample by altitude instead of by microphone and the plausible range stretches from 0.38 to 0.64, and Few is back inside it.
The paper isn’t careless. It says outright that thirty-nine microphones along one flight path aren’t thirty-nine independent experiments, and that the constant drifts with height. It just never follows that sentence to the conclusion it was about to publish. The drift is the finding. The constant changes by a factor of nearly two between the bottom of the path and the top. Either the boom takes a different share of the drag energy at different speeds, or the rule that turns a pitch into a width is off. I can’t tell which, and neither can the data.
One small thing fell out of the algebra and I liked it. The constant depends on the air’s pressure and density, and the paper lists bad atmospheric models as a possible cause of the drift. But pressure and density cancel. Only the speed of sound survives, and to fake this much drift the temperature would have to be off by a factor of three and a half. Whatever is going on, the weather didn’t do it.
I wrote to the author. The paper was accepted three days ago, so I don’t expect it to change. I’d just rather she hear it from a stranger now than from a referee on the next paper.
The part I keep thinking about isn’t about booms. Any average taken from people who happened to be standing somewhere is partly a map of where they stood. Twenty listeners on one road and ten on another isn’t a jury. It’s two neighbourhoods, and one of them is louder.
