# No sonic boom? Why not?

#### curtmorehouse

I read that the speed of sound in air at 20 degrees celsius is about 1126 feet per second.
When I shoot my rifle, there is a noticeable crack which I believe to be the 'sonic boom'. I also have 'sub-sonic' ammo that does not cause the CRACK, because the bullet is traveling slower than the speed of sound.

My question is, if I shoot an Air Rifle (bb gun) that shoots bb's at an advertised rate of 1400 feet per second, why is there no CRACK (sonic boom) ?

Is there a MASS requirement for me to hear the boom?

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#### A.T.

When I shoot my rifle, there is a noticeable crack which I believe to be the 'sonic boom'.
I don't think that you hear the sonic boom of a bullet that you have fired yourself.

When the round shockwave reaches your ears, you hear the "bang" from the shot. The conical shockwave behind the bullet that causes the sonic boom never passes your ears. They are inside the geometrically extended cone from the start (or behind the cone if you will). So the expanding cone surface (sonic boom shockwave) never passes them.

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#### fluidistic

Gold Member
because they are inside the cone.
Should be "because they are NOT inside the cone"?

Gold Member
No, he meant inside the cone. The sonic boom is a result of the pent up sound pressure at the shockwave coming off of the object (in this case the bullet). You start in an area where that shockwave will never cross your ears since it starts in front of you, effectively placing you inside the cone.

Of course, there is the shockwave generated at the barrel by the explosion, and that is where the difference is between the aforementioned guns. You are really just hearing the explosion and associated pressure wave, not the shock and sonic boom associated with the bullet. The bullet itself wouldn't have much of a sonic boom simply because it isn't putting much noise into the flow.

#### A.T.

Should be "because they are NOT inside the cone"?
No I meant inside the cone in more abstract geometrical terms (infinite cone). I modified the post to make it more clear.

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#### xts

For those of you who got some military training (don't try it with your riffles!): if someone shoots in your direction from the distance, then, as the bullet passes you by (so the boom cone should cross my ears):
1. subsonic bullets (e.g. pistol ones) are almost quite silent - that is pretty understandable;
2. supersonic bullets (e.g. from sniper's carabine) may be heard not as a single 'boom', but rather as a whistling sound, lasting for 1/2s or so - I don't understand the mechanism behind this whistle.

#### A.T.

2. supersonic bullets (e.g. from sniper's carabine) may be heard not as a single 'boom', but rather as a whistling sound, lasting for 1/2s or so - I don't understand the mechanism behind this whistle.
Well, they are not supersonic forever. So at large distance they might already gone subsonic. Also: The conic shock wave is affected by obstacles like vegetation and reflected by the ground. This might "blur" it.

#### xts

Well, they are not supersonic forever. So at large distance they might already gone subsonic.
True, but you hear 'whistle' rather than 'boom' when bullets are definitely still supersonic, e.g. if you are crawling on no-man's land, and your colleagues continue carabine fire over your head from a distance of 100m or so.

The bullet of 800m/s muzzle velocity, having effective range of over 1km, cannot slow down to subsonic on first 100m.

The blur by reflections from the ground seems to be convincing explanation...

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Gold Member
Bullets are tiny and fast-moving, meaning that the sound they generate will be high-pitched due to the fact that the perturbations they create in the air are small and high-frequency.

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#### chrisbaird

Bullets are tiny and fast-moving, meaning that the soun they generate will be high-pitched due to the fact that the perturbations they create in the air are small and high-frequency.
Excellent answer. Sonic boom just means that the sound generated by an object has piled up into a shock wavefront. But the sound does not magically appear because an object is going fast; it still must create the sound. An object that is very quiet at sub-sonic speeds (e.g. a bullet slicing through the air) will have a quieter sonic boom. Similarly, an object that creates high-pitched sounds normally will create a high-pitched sonic boom. The classic sonic boom heard when a supersonic jet passes overhead is the low-pitch roaring sound of the engines piled up so that it is much louder and sudden.

#### DaveC426913

Gold Member
Similarly, an object that creates high-pitched sounds normally will create a high-pitched sonic boom. The classic sonic boom heard when a supersonic jet passes overhead is the low-pitch roaring sound of the engines piled up so that it is much louder and sudden.
No, it seems to me, the whole thing about a sonic boom is that it is a single wavefront of pressure, not a sustained sound. Regardless of the length of an object (be it a face-on manhole cover or a jet plane) it creates a single pressure wave dependent on the area and on the velocity. i.e. sonic booms do not have a pitch, so small object do not make "high-pitched" sonic booms and large objects do not make "low-pitched" sonic booms.

(I grant that objects can create a multitude of shock waves, such as leading and trailing edges, but that does not change the principle that any given shich wave is a single pressure wave.)

#### cjl

Excellent answer. Sonic boom just means that the sound generated by an object has piled up into a shock wavefront. But the sound does not magically appear because an object is going fast; it still must create the sound.
Not true. The sonic boom appears exclusively because the object is traveling faster than the speed of sound. The object can be emitting no sound of its own, and it will still create shockwaves simply because it is traveling through the air faster than sound.

#### chrisbaird

Not true. The sonic boom appears exclusively because the object is traveling faster than the speed of sound. The object can be emitting no sound of its own, and it will still create shockwaves simply because it is traveling through the air faster than sound.
Perhaps we are getting into semantics, but I consider a shockwave a sound, therefore this statement is contradictory.

#### A.T.

sonic booms do not have a pitch, so small object do not make "high-pitched" sonic booms and large objects do not make "low-pitched" sonic booms.
I agree in respect to the initial wavefront. See the conical shock wave in the picture. This is not a "whistling sound, lasting for 1/2s or so". This is something you will hear as a crackle or loud click.

The whistling sound as described by xts is then heard in the cone and blurs with the initial crackle. But without actual recording we are just guessing around, about human perception.

#### cjl

Perhaps we are getting into semantics, but I consider a shockwave a sound, therefore this statement is contradictory.
A shockwave can be considered a sound of sorts, but your prior statement implied that the sonic boom was the result of other sounds emitted by the object traveling supersonically. For example, you claimed that jet aircraft creating a sonic boom did so because the sound of the engine "piled up". This is false - the reason jet aircraft make loud, rumbling sonic booms has more to do with their size and the resultant intensity of the shock wave produced, which is why (for example) the sonic boom created by the space shuttle during reenty sounds very similar to the one generated by the concorde, even though one of them has jet engines and the other is gliding when the boom is created.

Gold Member
No, it seems to me, the whole thing about a sonic boom is that it is a single wavefront of pressure, not a sustained sound. Regardless of the length of an object (be it a face-on manhole cover or a jet plane) it creates a single pressure wave dependent on the area and on the velocity. i.e. sonic booms do not have a pitch, so small object do not make "high-pitched" sonic booms and large objects do not make "low-pitched" sonic booms.
Any object moving supersonically will create shockwaves, but the shape and intensity most certainly is dependent on more than just the area. In fact, the area has very little to do with it and much more on the overall shape. For example, a sharper object creates a sharper Mach cone. A blunt object creates a bow shock. There are many things that play into it. However, the physical reason for a shockwave is what you aren't grasping.

An object moving through the air perturbs the air around it, which manifests itself as pressure fluctuations. These pressure fluctuations are sound. The wavelength (hence frequency) of these fluctuations depend on a great many things, but in particular an objects size, speed, shape and any noise-generating devices on the object. When the objects move faster than the speed of sound, these sound perturbations can't keep up and the ones moving forward start falling behind. As more sound waves are created, they coalesce with the previous waves and eventually form a shockwave. This shockwave most definitely will have a characteristic frequency to it based on what frequency the soundwaves generated by the object were before they coalesced. With a plane, you hear and feel an low boom. With a supersonic bullet, you hear and feel a much smaller and higher-pitched crack. Any sustained whistling afterwards is as a result of the sound created normally through the passing of the bullet through the air.

Not true. The sonic boom appears exclusively because the object is traveling faster than the speed of sound. The object can be emitting no sound of its own, and it will still create shockwaves simply because it is traveling through the air faster than sound.
True, and the frequency of that sound will be dependent on what frequency the perturbations generated by the object are. Smaller objects will generally have higher frequency sound (from things such as shed vortices). With a plane, the sound of the engines and other things just add to the effect (though it certainly won't do anything like double the effect or anything).

Perhaps we are getting into semantics, but I consider a shockwave a sound, therefore this statement is contradictory.
A shockwave is sound. However, you can generate sound purely aerodynamically as opposed to with engines.

#### DaveC426913

Gold Member
Any object moving supersonically will create shockwaves, but the shape and intensity most certainly is dependent on more than just the area. In fact, the area has very little to do with it and much more on the overall shape. For example, a sharper object creates a sharper Mach cone. A blunt object creates a bow shock. There are many things that play into it. However, the physical reason for a shockwave is what you aren't grasping.
I am grasping it quite fine.

An object moving through the air perturbs the air around it, which manifests itself as pressure fluctuations. These pressure fluctuations are sound. The wavelength (hence frequency) of these fluctuations depend on a great many things, but in particular an objects size, speed, shape and any noise-generating devices on the object. When the objects move faster than the speed of sound, these sound perturbations can't keep up and the ones moving forward start falling behind. As more sound waves are created, they coalesce with the previous waves and eventually form a shockwave. This shockwave most definitely will have a characteristic frequency to it based on what frequency the soundwaves generated by the object were before they coalesced. With a plane, you hear and feel an low boom. With a supersonic bullet, you hear and feel a much smaller and higher-pitched crack.
An object that is otherwise making no noise will still create a shock wave and thus a sonic boom.
An object that has a simple geometry, and a correspondingly simple shock envelope will still create a shock wave and thus a sonic boom.

As I pointed out, there are overtones, because real-wrold objects are not simple and silent, however, in principle the shockwave is a single pressure wave, and has no frequency.

When chrisbaird said this:
Sonic boom just means that the sound generated by an object has piled up into a shock wavefront.
he was wrong.

Gold Member
I am grasping it quite fine.
Clearly not based on the rest of your post.

An object that is otherwise making no noise will still create a shock wave and thus a sonic boom.
Objects moving through the air never make no noise. Just because you can't hear the noise doesn't mean it isn't being made. Even the tiniest of pressure fluctuations, which are present as a result of quite literally any object moving through a viscous fluid, are going to result in some degree of noise. This sound is what coalesces into the shock.

An object that has a simple geometry, and a correspondingly simple shock envelope will still create a shock wave and thus a sonic boom.
I don't believe anyone ever said it wouldn't. However, your originally said the shock was dependent on area (only sin a sense) and Mach number (it is), which was incomplete and partially incorrect. I was correcting this.

As I pointed out, there are overtones, because real-wrold objects are not simple and silent, however, in principle the shockwave is a single pressure wave, and has no frequency.
Not true. A shock is a pressure wave, as you put it, but it is a result of the coalescence of many sound waves, each one of which contains a frequency (it is sound after all). The very fact that it can be described in terms of a wave means it has a frequency. If it didn't have a frequency, you couldn't hear it. I could go on and on.

When chrisbaird said this:
chrisbaird said:
Sonic boom just means that the sound generated by an object has piled up into a shock wavefront.
he was wrong.
No he wasn't. The key point is that any object moving through a viscous medium produces sound. It doesn't just come from the engines or other similar sources.

#### xts

Two more points about 'whistling sound':

- I am not sure if it is 0.5s or 0.1s, but definitely it lasts long enough to be noticed as lasting, rather than single 'click'

- maybe the 'whistle' is somehow related to bullet rotation? Carabine bullets usually make one rotation every 25-35cm, which, at 800m/s gives 2-3 kHz. That might be a pitch of bullet 'whistle'. But, on the other hand the bullet is pretty symmetrical...

#### DaveC426913

Gold Member
Clearly not based on the rest of your post.
This is rude and uncalled for. Knock it off.

Objects moving through the air never make no noise. Just because you can't hear the noise doesn't mean it isn't being made. Even the tiniest of pressure fluctuations, which are present as a result of quite literally any object moving through a viscous fluid, are going to result in some degree of noise. This sound is what coalesces into the shock.
The point is that the noise is incidental. A single pressure wave - one compression - is enough to be a shock wave. That is the essence of a shock wave, regardless of the details you've mentioned.

Gold Member
This is rude and uncalled for. Knock it off.
Then stop claiming you know things based on what appear to be (educated) guesses.

The point is that the noise is incidental. A single pressure wave - one compression - is enough to be a shock wave. That is the essence of a shock wave, regardless of the details you've mentioned.
Noise is not incidental. Noise is the source of the shock. One compression is not necessarily enough to be a shock. It has to be of such a strong magnitude that certain properties are effectively discontinuous across the shock (in reality, a shock is of finite thickness, but so tiny that it can be treated as infinitesimal). This happens when a whole bunch of sound waves (which are incidentally smaller compression waves but not shocks) coalesce. In the case of an object moving through the air, this is because the sound emitted by the object cannot keep up with the object and the sound waves coalesce (see image).

The shock is sound, therefore it has a frequency (or pitch) associated with it based on the sound that generated it. If this wasn't true, the sound made by a bullet would not differ from that made by a plane save in magnitude

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#### A.T.

The shock is sound, therefore it has a frequency (or pitch) associated with it based on the sound that generated it.
Here is the caption of the animation you posted, taken from:
http://en.wikipedia.org/wiki/Doppler_effect
The sound source has now broken through the sound speed barrier, and is traveling at 1.4 times the speed of sound, c (Mach 1.4). Since the source is moving faster than the sound waves it creates, it actually leads the advancing wavefront. The sound source will pass by a stationary observer before the observer actually hears the sound it creates. As a result, an observer in front of the source will detect
Try different values for f0 and see if it affects f.

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Gold Member
That equation isn't correct though. $c-v_{s} \not= 0$, so $f \not= \infty$.

Of course, that equation isn't even valid when you reach Mach 1, so you really can't take anything on Wikipedia as automatically true.

Of course, I may be slightly off in my explanation. Perhaps it is better to say the shock doesn't have a frequency, per se. The higher frequencies generated by a smaller object will still be heard just behind the shockwave and would explain the whistling and the smaller sound of the shock is probably better explained by the smaller pressure wave generated by a small object on account of less air being displaced. My mistake.

Still, any sound source on the object will add to the shock since the radiated sound will be of greater magnitude; it just won't add that much.

#### bbbeard

Objects moving through the air never make no noise. Just because you can't hear the noise doesn't mean it isn't being made. Even the tiniest of pressure fluctuations, which are present as a result of quite literally any object moving through a viscous fluid, are going to result in some degree of noise. This sound is what coalesces into the shock....

Not true. A shock is a pressure wave, as you put it, but it is a result of the coalescence of many sound waves, each one of which contains a frequency (it is sound after all). The very fact that it can be described in terms of a wave means it has a frequency. If it didn't have a frequency, you couldn't hear it. I could go on and on.
The physical picture you are promoting, that (a) a shock wave is the result of the coalescence of small perturbations, and that therefore (b) the shock wave retains some kind of information from the source of the perturbations, is incorrect.

Consider that the typical sonic boom is the result of the passing of the oblique shocks attached to a supersonic object. In the frame of the object, the atmosphere (quiescent in the earth frame) is approaching uniformly at the flight speed of the object. The oblique shock arises from the need to turn the flow in a way that is compatible with the physical requirement that pressure waves can only travel at the speed of sound. Shocks are nature's way of matching upstream and downstream boundary conditions when the upstream flow is supersonic. There is also typically an oblique shock at the tail of the object, as the flow has to straighten out again.

Shock layer thickness is equal to only a few mean free paths. In practical terms this means that the shock is a step function. The Fourier transform of a step function goes like -i/omega, so it has contributions from all frequencies. There is no substructure that incorporates tiny oscillations emanating from the supersonic body. In fact shock are highly dissipative; they destroy information and generate entropy.

Sonic booms incorporate the pressure jumps from both the tip and tail of the flying object. Consider the shock structure for the paradigmatic diamond-wing airfoil. If the flight Mach number is sufficiently high, there is an attached oblique shock at the tip. There will be a Prandtl-Meyer expansion fan at the mid-chord corner, which allows the flow to accelerate around the corner. And then there is a compression shock at the tail as the flow has to straighten out again. On the ground, the timing of the shocks will depend on the length of the object, its altitude, and its flight speed. The typical sonic boom is the result of the passing of this "N wave". Larger objects create a bigger lag between tip and tail and may be experienced as a lower-pitched boom, although the shocks themselves are step functions.

#### bbbeard

Noise is the source of the shock.

Taken from Wikimedia commons.
The animation you linked from Wikipedia is mislabeled. I have informed the author and I hope he corrects this mistake.

The pretty picture labeled "sonic boom" is not a boom and is not really even a shock wave. The oblique wave you see in the picture is properly called a "Mach wave" and is equivalent to an oblique shock in the limit of zero strength (i.e. no turning of the flow and no rise in pressure). You can create a Mach wave in a wind tunnel by roughening the surface of a test specimen and the perturbations in flow will propagate and coalesce, very much like your description of shock waves. However, you would hardly notice the passage of a Mach wave, because there is no static pressure rise such as the rise you get across a true shock.

However, shock waves do not require the coalescence of perturbations to form. An oblique shock will form in a supersonic flowfield pretty much whenever the flow has to turn compressively (i.e. into itself). A normal shock will form when a supersonic flow needs to change speed abruptly without turning. The F-16, famously, has a normal-shock inlet which slows the flow abruptly from supersonic to subsonic to enable it to be further slowed down in the subsonic diffuser. These "true" shocks -- as opposed to Mach waves -- have nothing to do with coalescence of tiny perturbations.

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