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If someone is flying just above Mach 1 for 10 minutes, I would think the sound/shock waves would just pile up and gain more energy, resulting in a very intense and loud boom when the pilot slows down.

However, I don't think this is the case. I saw one answer online, that said it would not, but it did not explain why. Even if it doesn't happen, I don't understand how ten seconds of sound waves behind you piling up would be the same shock intensity as ten minutes of supersonic flying.

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    $\begingroup$ I'm imagining a boat, cruising across a lake, with a progressively larger wake until there is dry land behind the boat. Maybe that's what Moses did? $\endgroup$
    – tedder42
    Sep 29 at 13:03
  • $\begingroup$ @tedder42 No, Moses was never reported to have gotten into the water prior to it parting ;) $\endgroup$
    – Ahmed Tawfik
    Sep 29 at 14:12
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    $\begingroup$ Unfortunately air and the sound waves moving in it are invisible. But luckily in nature waves exist that can be actually easily seen. These are the waves generated by perturbations at the interface between a liquid and a gas: the waves generated by a duck swimming in a lake 😅 I think that watching those waves generated by a duck or a boat is the best way to understand Mach cone and other supersonic concepts 🖖 $\endgroup$
    – sophit
    Sep 30 at 2:29
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    $\begingroup$ Well, actually, you can see the transonic vapor cone. It now makes sense to me. Thank you. $\endgroup$
    – DaCuteRaccoon
    Sep 30 at 20:08
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    $\begingroup$ @tedder42 And now I can't get the image of Charlton Heston, playing George Washington, crossing the Delaware River in a speedboat going Mach 9 out of my head. $\endgroup$
    – End Anti-Semitic Hate
    Oct 1 at 4:34

3 Answers 3

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They don't really pile up like that. The 'pile up' description of how shock waves form is pretty flawed.

The shock wave forms at an angle off of the body. Generally speaking, it forms a cone off of the nose of the body. Technically, there are usually two cones, one from the nose, the other from the tail caused by the air coming back together again.

As the aircraft flies forward, the cones sweep out a footprint on the ground. When the cones pass over you, you hear the boom.

The aircraft's lift contributes to the strength of the boom. So, the boom will actually be slightly weaker at the end of the mission (because a bunch of fuel has been burned off).

When the aircraft turns, it can create regions of a stronger and weaker shock. First, the lift is increased during a turn. Second, the turn causes the shock to spread out (on the outside) and squeeze together (inside of the turn). This causes some boom focusing and can strengthen the boom.

The atmospheric conditions between the boom causing aircraft and the ground can have an effect -- winds, temperature, humidity, etc. can change how the boom propagates. An aircraft could take off in conditions that dissipate the boom, but at the end of the mission could be somewhere where the boom propagates with fewer loses -- and would therefore be perceived stronger.

When an aircraft slows down at the end of a mission, the strength of the boom changes and this can also cause some focusing like a turn. Similarly, if the aircraft dives or climbs, it can cause focusing or spreading of the boom.

So while the shock waves don't pile up in the sense of accumulating throughout the mission, they can interact in complex ways to affect the strength of the shock from the aircraft.

Engineers working on low boom aircraft not only study the shape of the aircraft, but also the propagation of the boom to the ground and the trajectory the aircraft will follow. It may be that turns are planned to focus the boom in unpopulated areas, or deceleration / descent at the end of missions is done offshore before coming over land... There are many interesting challenges to be considered.

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    $\begingroup$ What about altitude? I used to hear that flying higher didn't help because it just spread the boom farther out but that it was just as loud. Which always seemed counterintuitive because there is a fixed amount of energy. I have since heard that altitude does decrease the boom somewhat. I also heard that the boom is much louder directly underneath the flight path, and less jarring if farther away. Which would explain people in the UK who said they could hear the sonic boom from Concorde when it was approaching the coastline and that it wasn't that bad. $\endgroup$
    – Steve Pemberton
    Sep 29 at 6:51
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    $\begingroup$ Trust your intuition. The same way any sound grows faint the further you are from it, sonic boom effects are less the higher the airplane is. $\endgroup$
    – Michael Hall
    Sep 29 at 14:33
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    $\begingroup$ @StevePemberton: Perhaps that's a distortion of some actual facts: It wasn't possible to fly high enough for the boom not to be a problem directly under the flight path (at least for Concorde). And more people could hear the boom at all if flying higher, even though the sound power was more spread out for all of them. $\endgroup$
    – Peter Cordes
    Sep 29 at 15:23
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    $\begingroup$ @MichaelHall - to some extent yes. But when it comes to fluid dynamics I try not to rely too much on intuition. While the things being said were counterintuitive, I held off dismissing them until I got some confirmation that things worked a little more as expected in this regards. As Rob McDonald's answer illustrates, there are many factors that can affect the strength of a sonic boom for a particular location at any one moment. I'm interested in quantification of the effects of altitude and distance which is somewhat hard to come by. Which is understandable because of the many variables. $\endgroup$
    – Steve Pemberton
    Sep 29 at 16:05
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    $\begingroup$ @StevePemberton Altitude certainly makes a difference -- in particular the temperature layers of the atmosphere the boom must go through. If you are only slightly supersonic -- say Mach 1.1 at altitude, where the air is very cold, by the time the shock wave reaches sea level, that speed might not be supersonic anymore and the boom will actually go away. Yes, the groundtrack boom is stronger than the off-groundtrack (unless there is focusing from turning, etc). $\endgroup$
    – Rob McDonald
    Sep 29 at 17:17
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Even if it doesn't happen, I don't understand how ten seconds of sound waves behind you piling up would be the same shock intensity as ten minutes of supersonic flying.

Sound is pressure, and sound is energy. If someone hears the sonic boom, that's because energy from the shockwave is leaving the vicinity of the airplane, and reaching the ground. If it were to "pile up" for 10 minutes and then suddenly all be released, BOOM, that would mean that nobody would hear anything for the first 10 minutes, and obviously that isn't what happens.

So, the "piling up" explanation is really pretty misleading. What it really means to be supersonic is that pressure waves can't travel forward relative to the airplane, only backward. Since pressure waves can't travel forward, there can't be a gradual change in pressure, or a gradual redirection of air around the body. Instead, it happens suddenly, in a very short distance, which is the "piling up" that forms the shockwave. But the shockwave still moves away from the airplane: up, down, to the sides, and especially backwards. When it reaches an observer, they hear a boom.

The airplane is constantly feeding energy into the shockwave by disturbing the air (and it gets that energy from the thrust provided by its engines), and the shockwave is constantly carrying energy away. In general, the two processes are in equilibrium — the shockwave is carrying away just as much energy as the airplane is putting in. There's no continuous buildup.

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    $\begingroup$ I think the "pile up" analogy would be fine if one couples it with an image of trying to dump a continuous stream of sand onto a tower's flat roof. After awhile, the amount of sand on the roof will stabilize at some limit where the rate at which sand flows off the roof has increased to match the rate at which it is applied. $\endgroup$
    – supercat
    Sep 29 at 17:46
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So, the "piling up" explanation is really pretty misleading. What it really means to be supersonic is that pressure waves can't travel forward relative to the airplane, only backward.

This does not mean air directly in front of the nose would travel backwards relative to the plane. Then the air would be in the nose and the nose would be broken.

There's no continuous buildup.

There is a buildup. It's just not a buildup of sonic boom. The skins of supersonic aircraft get hot and must be cooled to remove the buildup of heat. The cooling could be infrared radiation. In the case of the SR-71, the heat was transferred to the fuel. When the aircraft slows down, some of the heat stored in the skin is released.

These details may help explain the sonic boom better, in addition to the other answers:

  • Compressing air stores energy in both compression and heat. Some of the heat is transferred to the plane.
  • Air can travel faster than the speed of sound. Molecules that have just been hit by a supersonic aircraft are very likely to be going faster than the speed of sound. Their motion is partly random. The motion of the molecules relative to the plane prevents them from accumulating on the front of the plane. As mentioned by hobbs, the shockwave moves to the sides.
  • If you are on the ground listening to a passing supersonic aircraft, you hear a boom. The sound waves produced by the aircraft long before it passes are weak. The sound waves produced by the aircraft long after it passes have not arrived yet when you hear the boom. As a result, the boom you hear from the ground mostly comes from a brief period of flight.

  • When the cones pass over you, you hear the boom.

Another way to say this is that the boom exists before and after you hear it, but you only hear it when it is at your location.

  • The total energy in the shock cone does increase the longer you fly. However, since the cone gets bigger, the energy is spread out more. It will "intensify" globally, but local measurements of loudness will not increase.

  • Fluids are more complicated than line drawings.

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  • $\begingroup$ Re "The total energy in the shock cone does increase the longer you fly." -- really? I'm more inclined to believe last paragraph of this answer -- aviation.stackexchange.com/a/101084/34686 $\endgroup$
    – quiet flyer
    Sep 29 at 23:19
  • $\begingroup$ @quietflyer I agree with the last paragraph of that answer, so long as it refers to the energy density. There is no contradiction. $\endgroup$
    – Anonymous Physicist
    Sep 30 at 12:59

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