# What exact speed point does shock wave start to appear

1. Dec 6, 2013

### taregg

what exactly speed point does shock wave will start to appears..

2. Dec 6, 2013

### taregg

and please can you write down the velocity speed ln m/s or km/h....

Last edited: Dec 6, 2013
3. Dec 6, 2013

### stevendaryl

I think "shock wave" has several meanings, but one type is a sonic boom. That happens when an object travels at the speed of sound (or passes through the sound barrier from slower than sound to faster than sound). The reason for the sonic boom is that if a source of sound is traveling through the air at speed $v$, then the frequency of the sound wave will be Doppler-shifted from frequency $f$ to frequency $f'$ given by:

$f' = \dfrac{f}{1-\frac{v}{c_s}}$

where $c_s$ is the speed of sound. When $v = c_s$, the Doppler-shifted frequency goes to infinity.

4. Dec 6, 2013

A shock wave isn't just formed when "passing through the sound barrier". It forms and is constantly maintained any time air is moving greater than the speed of sound relative to the body/vehicle.

In other words, there is no set speed. All that is required is that the flow velocity be Mach 1 or higher somewhere on the body in question. That's easy enough to calculate, as for most reasonable conditions, the speed of sound in air is a function of only temperature. It is complicated slightly by the fact that you can have, for example, a plane traveling at say Mach 0.8 and due to locally accelerated flows over the wings you can still get shock waves if it at any point accelerates to Mach 1 locally.

Just for reference, the speed of sound in air at sea level is approximately 340 m/s.

5. Dec 6, 2013

### stevendaryl

I'm wrong, but it's sort of interesting to go through why I'm wrong.

The way I was thinking about it was this: Sound is a traveling compression wave, alternating higher than normal pressure and lower than normal. If the source of the sound is traveling at exactly the speed of sound, then the high pressure waves produced at different times will undergo constructive interference. So the crests from sounds produced at different times will arrive at the listener simultaneously, leading to a sudden change from normal pressure to extremely high pressure. (This corresponds to the point of infinite Doppler shift.)

My reasoning was that if the source of the sound is traveling faster than the speed of sound, then the crests won't arrive together: the sounds that were produced later will arrive earlier--the crests arrive in reverse order, but shouldn't be any higher amplitude than sounds produced by a stationary source.

Why this is wrong is that it is only taking into account one-dimensional motion. For sounds traveling at an angle $\theta$ relative to the motion of the sound source, the relevant speed of the source is the component of the source's velocity in the direction of the sound propagation. The full Doppler shift formula, taking into account angle, is:

$f' = \dfrac{f}{1 - \frac{v cos(\theta)}{c_s}}$

If $v > c_s$ ($c_s$ is the speed of sound, $v$ is the speed of the source), then there will always be some angle $\theta$ for which the Doppler shift will be infinite. If the listener is stationary, then the angle $\theta$ is constantly changing, so there will be some point where the sonic boom will be heard.

I think that's correct.

6. Dec 6, 2013

### rcgldr

A shock wave occurs when the decible level reaches the point that the peak pressure is greater than 1 atm, producing a non-sinusoidal save, since the minimum pressure is 0 atm. Any object moving faster than the speed of the sound relative to the air stream is going to generate a shock wave. A shock wave will transition into a regular sound wave over time, and this is the sonic boom that is heard. If the shock wave is heard, it sounds like a loud crack instead of a boom. Example video of a F14 super-sonic flyby (windows movie file), the sound is heard in the second fly-by in the video:

http://rcgldr.net/real/f14flyby.wmv

7. Dec 6, 2013

This is absolutely, positively not the definition of a shockwave you can and often do have pressures on the high pressure side of a shock wave that are well above 1 atm, and you can and often do have pressures on the high pressure side of a shock wave that are well below 1 atm.

A shock wave is a discontinuity in some quantity (or near discontinuity if you include enough nonlinear terms in your model), in this case pressure, temperature, density, etc. Essentially, when you have a sound wave traveling through a medium, the compression it causes results in a very minute change in flow properties, including temperature. That means that under the right conditions, if another sound wave is following behind closely enough before the temperature finds its way back to the value around it, the second wave will be traveling ever so slightly faster and eventually catch up with the first wave. When a body is moving through a flow at supersonic speeds, this happens, and it happens with many sound waves. With all these sound waves catching each other, you end up with a nearly discontinuous change in flow properties along the point where they meet, called a shock wave.

The actual jump in properties across that wave depends on the Mach number. If you had a body traveling close to Mach 1, the jump in pressure across the wave would be almost nonexistent, but what small jump was there would be effectively discontinuous. It need not jump to over 1 atm to be a shock wave, and in fact, many do not.

While a shock wave will definitely dissipate as the distance from the body increases, it doesn't simply transition into a sound wave. Once the shock wave forms, the only means by which it can dissipate are by slowly losing energy and the discontinuity essentially "closing". The sonic boom itself is not this dissipated wave, but the original shock wave itself. The intensity of the boom has to do with the fact that the shock causes the pressure to rise so fast (nearly discontinuous, after all). The actual pressure rise involved in a typical sonic boom on the ground is actually only a few pounds per square foot, yet it is still very loud.

The different between a crack and a boom has to do mostly with altitude (shock waves spread out and weaken as the propagate away from the plane) and the size of the aircraft (larger and heavier craft generate stronger booms). Thus, a supersonic bullet makes a crack while an F-15 makes a boom.

8. Dec 6, 2013

### rcgldr

Perhaps there are two definitions of a shock wave, or one describes the physics and the other describes how they are created:

Wiki articles and quotes from those articles:

Shockwave (distorted sound waves > 1 atm; waveform valleys are clipped at zero pressure)

wiki_sound_pressure_levels.htm

Over longer distances a shock wave can change from a nonlinear wave into a linear wave, degenerating into a conventional sound wave as it heats the air and loses energy. The sound wave is heard as the familiar "thud" or "thump" of a sonic boom, commonly created by the supersonic flight of aircraft.

http://en.wikipedia.org/wiki/Shock_wave

The F-14 in this video is about the same size as an F-15 and it's clearly making a crack, due to the closeness of the F-14 to the observers:

http://rcgldr.net/real/f14flyby.wmv

9. Dec 7, 2013

### taregg

ok..what about the blast wave that created from the shock waves..

10. Dec 7, 2013

There are not, to my knowledge, two definitions of shock waves. That Wikipedia article is just that: a Wikipedia article. There is nothing in any body of scientific literature that states that a shock wave must create a peak pressure greater than 1 atm to be considered a shock wave. In fact, 1 atm is completely arbitrary in terms of the grand scheme of the universe. The vast majority of shocks do not have a pressure that high on either side of them, for example the termination shock at the edge of the heliosphere or the shocks that form as a result of supernovae far from the actual point of explosion. Or if you prefer our atmosphere, the bow shock in front of the SR-71 flying at Mach 3.3 at 85,000 feet altitude would encounter a pressure of some 2.2 kPa (0.3 psi). Across that shock, the pressure would jump pretty drastically and immediately by a factor of about 12.54, but the pressure behind the shock is still a measly 27.59 kPa, or about 4 psi, well below 1 atm.

Again, this is a Wikipedia article. In a mathematical sense, it is impossible for a shock wave to degenerate into a linear wave once it truly becomes a shock. I suppose it would be potentially in the realm of possibility for a physical shock wave to do this if only because this is nature, and there are no actual multi-valued solutions in nature (quantum mechanics notwithstanding), so if you include enough nonlinear terms in the mathematical model, the shock is not truly, mathematically speaking, a shock. However, I have never once in my career studying aerodynamics heard of an instance of this occurring and it will take more than a Wikipedia article (read: scientific evidence) to convince me that it happens.

The reason a shock wave created by a high-altitude plane actually dissipates is not that it coverts into a sound wave, but that, through the changing atmospheric conditions and through interactions with the body's own Mach waves, the leading shocks will bend in toward the body. As they bend in, they become weaker (a natural result of oblique shock theory) and eventually upon reaching the limit of being horizontal, cease existing. If a ground observer does not hear a sonic boom, it is likely because the object making the shock wave is high enough that the shock system bends completely horizontal and therefore dissipates completely before reaching the ground.

Yes, and the reason is not that the shock passes over your ear as opposed to a sound wave. More likely the difference is because the shock is much stronger at that point (as opposed to being 30,000 feet below the plane and has not refracted much at all, so you get a much sharper boom followed by a slight rolling noise afterward due to the sound reflecting off of the various surfaces and the waves.

11. Dec 7, 2013

I am not really sure what you mean here. A blast wave is typically just a shock wave resulting from an explosive that detonates such that the pressure wave expands supersonically from the blast center behind a shock. By definition, then, a blast wave is preceded by a shock.

12. Dec 7, 2013

### rcgldr

I meant the local ambient pressure (the pressure at current altitude), not the absolute pressure constant for sea level air.

13. Dec 7, 2013

### taregg

but what i mean exactly...what is difference between shock waves that from supersonic jet and from high explosive bombs...

14. Dec 7, 2013

Well that's not the definition of 1 atm. What you have just described here is the notion that the shock, when passing, must simply increase the pressure above ambient pressure. This is definitely true of a physically realizable shock, but many other thing scan do this as well, including simple sound waves.

A shock definitely has to increase the static pressure as it passes. The opposite (a so-called expansion shock) is mathematically admissible but violates the second law of thermodynamics, and so never actually occurs. So, even though a shock must definitely cause a pressure rise, this is not sufficient condition for the existence of a shock, as even a simple sound wave can pass through a medium and raise the pressure behind it to above that of ambient. The important criteria for the rise to be associated with a shock wave are that the local pressure, density and temperature must increase and they must do so discontinuously.

What you originally typed was that the peak pressure reaches 1 atm while the minimum is 0 atm, "producing a non-sinusoidal wave". Based on what you just said, are you actually trying to say that this minimum of 0 atm is gauge pressure (i.e. measured as a differential pressure against the local ambient pressure)? If so, then are you using atm here to represent the pressure of the local ambient pressure? If that is the case, what you are saying is that the absolute ambient pressure is $p_a$ and a shock forms when a wave passes by that raises the absolute pressure to $2p_a$. This is also not true. You can have a shock raise the ambient pressure to $1.001p_a$ (which happens when the Mach number is 1.000428) just as easily as you can have it raise the ambient pressure to $40p_a$ (at Mach 5.87).

Nothing. They are the same phenomenon.

15. Dec 7, 2013

### rcgldr

I think the key point of the wiki statement is that clipping of what would otherwise be a sine wave that occurs at zero pressure, which coexists when peak pressure is greater than double the ambient pressure, and that's considered to be a shock wave. Perhaps there are other forms of shock waves, but that is description used in that wiki table.

16. Dec 7, 2013

That Wiki explanation makes no sense though. First, there is nothing saying a sound wave has to be sinusoidal. Second, nothing says that the mean pressure about which a sound wave is centered (were it actually sinusoidal) has to be at ambient pressure. Neither of those are true, so that purported definition of a shock wave is not true. It's one of many examples of questionable things being written on Wikipedia.

17. Dec 7, 2013

### rcgldr

It's not just wiki:

http://www.lasalle.edu/~reese/decibels.htm

Sound-Pressure-in-Air.pdf

http://medlibrary.org/medwiki/Sound_pressure_level

Regarding shock wave dissipation into a sonic boom sound wave (as opposed to the crack of a shock wave):

... the accompanying expansion wave approaches and eventually merges with the shock wave, partially cancelling it out. Thus the sonic boom associated with the passage of a supersonic aircraft is the sound wave resulting from the degradation and merging of the shock wave and the expansion wave produced by the aircraft.

princeton_shock_wave.html

18. Dec 7, 2013

All of those sources were literally copied from Wikipedia. The first three were identical tables that cite no sources and are exactly the same to the word as the Wikipedia table. They also aren't from any kind of aerospace- or fluids-related sources so I have no reason to trust that it was the original source. One is a music professor. One is like a neighborhood association for some neighborhood. The last is cited as a direct copy/paste from Wikipedia.

At any rate, the physics dictates that this isn't correct. Sound waves are not necessarily sinusoidal and are not necessarily centered on zero gauge pressure. In fact, they most often manifest as solitary propagating pressure peaks and have no true valley, but rather a rather slow relaxation back to ambient pressure. When many of these peaks coalesce into a discontinuous pressure jump, that is a shock wave.

If you still truly believe this, then explain my example earlier where you an have a shock where the pressure jump does not double the absolute pressure as you claim is necessary.

The Princeton one is also a direct copy/paste from Wikipedia and is cited as such. It's just some computer science graduate student copying the page for some unknown reason.

19. Dec 7, 2013

### AlephZero

I'm not sure another "anecdote" is going to convince you, but in a high bypass turbofan, flow through the fan blade tips is transonic, and we certainly worry about the location of shock waves.

But the overall pressure increase from inlet to outlet is only about 2 psi. (If that number seems unfeasibly small, a pressure of 2psi over an area over a 100 inch diameter circle generates quite a lot of thrust.).

So where are your alleged pressure increases of more than 15psi in the shocks coming from? Nowhere. They don't exist.

The basic cause of shocks is very simple. If the flow speed is faster than the speed of sound, any pressure variations downstream can't propagate back upstream to "even out" the global flow pattern. The place where they "get stuck" trying to go upstream is the shock. That's all there is to it. There is no "minimum pressure difference" required. The rest of the subject is just explanations of what the shock wave patterns around particular objects look like (with no offense meant to CFD gurus, of course!)

20. Dec 8, 2013

### rcgldr

The 2 psi jump is in the direction of flow that is nearly perpendicular to the direction of the rotating blades. The pressure at the stagnation zones on the leading edges of the blades would be higher.

Another article with a reference to shock wave and their assymetry, in this case for a focused sound field, unrelated to the tables linked to in previous posts:

535_1.pdf