# Do launching rockets produce a sonic boom?

I've been watching rocket launches, and the commentator often remarks when the vehicle has gone supersonic. There is presumably a sonic boom at this point, right? Is it just that we don't hear it on the ground because the engines are louder, and overpower the sound?

Definition of terms: A shock wave by itself is not a "sonic boom". A sonic boom is an event, produced by the shock(s) passing over something - an observer, a building, the ground. The "boom" is characterized by a rising/falling/rising pressure disturbance called an "N-wave" because the disturbance has the shape of an N when plotted. A model in a supersonic wind tunnel produces a shock wave but not a boom. Shock waves in rocket engine exhaust would not be called "sonic booms" either.

A sonic boom is heard by observers when the shock wave(s) produced by an object moving at supersonic speed passes by them. This is unlikely to happen with a rocket launch since the vehicle is at high altitude and moving away. The rocket produces a shock wave once it goes supersonic, but it probably won't pass by any observers.

Shuttle produced sonic booms on landing which could be heard by ground observers.

• "The shock wave must interact with something - an observer, a building, the ground - to produce the "boom". " That's not true. The pressure gradient (i.e. boom) is there, whether there's something to interact with or not. I'm reminded of philosophical statements like 'if a tree falls in the forest and there's nobody there to hear it, does it still make a sound?'. – Hobbes Jun 25 '19 at 15:41
• Thanks, edited to clarify. – Organic Marble Jun 25 '19 at 16:36
• Re, "...the vehicle is at high altitude and moving away." Might be worth mentioning that rockets (not counting weapons fired in conflict) are virtually never launched over any populated area. – Solomon Slow Jun 25 '19 at 17:20
• As the old proverb goes, "If a rocket produces a shock wave in the air, and nobody is around to hear, does it produce a sonic boom?" Or something like that. – Greg Jun 25 '19 at 19:59
• Considering that there are other ways to observe and record sound than our own ears and brain (think microphones and connected recording equipment as the most obvious candidates), I'm not sure this hair-splitting is really warranted. :-) – Gábor Jun 26 '19 at 13:25

Yes, it produces a sonic boom. But the shockwave travels in the same direction as the rocket (i.e. up) and doesn't reach the ground.

• Question bullets make a sonic boom and its possible to hear that from behind the shooter, wouldn't rockets be the same/ – Charlie Brumbaugh Jun 25 '19 at 23:58
• Bullets are generally fired at ground level and horizontally. So there are lots of objects for the shockwave to reflect off of and get back to the shooter. A rocket reaches supersonic speed a few km above ground, its shockwave has far fewer opportunities to be reflected. – Hobbes Jun 26 '19 at 6:06
• @Hobbes - So a bullet fired in midair is silent? – slebetman Jun 26 '19 at 10:52
• @slebetman if a tree falls down in the forest and there's nobody to hear, does it make a sound? – jwenting Jun 26 '19 at 11:22
• @CharlieBrumbaugh In addition to reflections, there is a discontinuation when the bullet leaves the barrel. That causes a different kind of loud sound than the bullet passing by, and it would travel circularly in all directions as the trailing wave is not yet there to cancel it. – jpa Jun 26 '19 at 11:26

Think about what a sonic boom is. It's the shock wave caused by 'bunching up' of the compression waves of the body, moving through the air.

To see this, consider:

• For a stationary body emitting pressure waves, at any one point in time you only hear the sound emitted at another (slightly older) point in time.

• However if the body is moving faster than the speed of sound, you can be hearing the sound form the body at multiple points in time. An observer see these waves getting bunched up and interfering as the waves from the body go back and meet older waves travelling forward. This 'bunching up' is what causes the boom.

However, if you start behind the body, before it starts moving, all the sound waves hit you strictly in order so you never experience the bunching up.

Hence no boom. You still hear the sound waves that make up the boom, you just don't hear them all at once as a sonic boom.

• This is the clearest and best explanation; hope it's the right one. – antlersoft Jun 26 '19 at 16:56
• @antlersoft: Thank you. There is a lot of over-simplification to this. The interaction of the compression waves ahead of the body and as they propagate out is complex (its not obvious there should ever be a boom), but the basic idea that the waves have to be able to "catch" each other to interfere and add up is correct. As is that: while this only happens behind the current position of the body, it only happens ahead of where the body started emitting pressure waves. Hence no boom behind the starting position. – ANone Jun 27 '19 at 10:05

No, to hear a sonic boom, the object must not only be traveling faster than the speed of sound, but also it must be traveling towards you.

If an object is moving towards you at less than the speed of sound, then the Doppler effect will cause you to perceive any sound it’s making as being a higher frequency. If it’s moving towards you faster than the speed of sound, you will perceive sound coming from the object as being reversed: since the object is coming towards you faster than the sounds it’s making, the later sounds it makes will reach you first, while earlier ones, traveling at the lower speed of sound, will reach you later. If the object is traveling at exactly the speed of sound, then all of the sounds it makes will reach you at exactly the same time, in a massive blast of sound.

If an object is not traveling directly towards you, then the speed at which it is approaching you is different from its full velocity. For instance, if a plane is one distance unit above you, and traveling with a horizontal velocity of $$v$$, then the distance between you and the plane is $$\sqrt{v^2t^2+1}$$, and the derivative of this is $$\frac {v^2}{\sqrt{v^2t^2+1}}$$. This is not constant: it goes to $$v$$ as $$t$$ goes to $$\pm \infty$$, but decreases the closer the object gets, and goes zero and changes sign when $$t=0$$ (for negative $$t$$, it’s coming towards you, for positive $$t$$ it’s going away from you). This is why the Doppler effect will result in different tone changes when a plane travels over you: it’s based on the derivative of the separation of the observer and emitter, not the velocity of the emitter.

So if an object is traveling at a velocity faster than the speed of sound, there will be some point at which its effective speed towards you is exactly the speed of sound. At that point, the Doppler effect (the instantaneous ratio between the time between sounds that object is making and the time between when you hear those sounds) will go infinite. The sounds it makes around that time will arrive at the same time, creating a sonic boom.