74

The speed of sound increases with increasing pressure. Assuming ideal behaviour the relationship is: $$ v = \sqrt{\gamma\frac{P}{\rho}} $$ or equivalently: $$ v = \sqrt{\frac{\gamma RT}{M}} $$ where $M$ is the molar mass. In a gun barrel just after the charge has gone off the gas is under very high pressure and very hot, so the speed of sound is much ...


55

I don't understand why exactly it leads to a powerful explosion instead of just a burst of ionising radiation. This radiation, representing most of the initial energy output by a nuclear weapon, is swiftly absorbed by the surrounding matter. The latter in turn heats almost instantly to extremely high temperature, so you have the almost instantaneous ...


38

Deflagration means that the combustion moves through the fuel slower than the speed of sound in the fuel. It doesn't say anything about the speed of the resulting gas, or how it compares to the speed of sound in that gas (and the speed of sound in solids is generally higher than that of gasses). The gas that is released from the combustion isn't at ...


22

In an implosion fission bomb, the bulk of the nuclear reactions (100 GJ) occur in the final microsecond--it is a tremendous amount of power--$10^{17}$ Watts. This power is dumped into the compressed Pu pit--which is a few kilogram with a density of 100 g/cm^3-it is small. The nuclear material is heated to an extremely high temperature, tens of millions of K-...


15

Update with a more clear answer: Here's a plot of all the velocities involved with shock propagation through a sationary medium: The x axis is the mach number of the shock wave and represents the strength of the shock wave, it could have been velocity or pressure ratio or any other quantity that is monotonic with shock strength. The y-axis is velocity ...


15

Your question seems to imply that you think that, over a deep-ocean tsunami where the wave is travelling at speeds in excess of the speed of sound in air, the water in the wave is travelling faster than that speed of sound. This is not the case. The wave is travelling faster than the speed of sound in air, but the wavelength of the wave is so long that the ...


10

The overall effect (in particular with regard to this light emission, which really happens – it's not just apparent) is mostly investigated under the name sonoluminescence. Though the process of this luminescence itself remains unsettled, it is for sure that extremely high temperatures are produced at a bubble collapse (in fact, it was conjectured they ...


9

The reason that the speed of sound is a well-defined quantity is that, for small pertubations, the equations which govern the fluid dynamics can be linearised. In that linearised form, the solution boils down to a simple wave ansatz with linear dispersion relation, i.e. constant velocity.Those are the sound waves. It so happens that in air, this linear ...


9

Short Intro The nonlinear term or steepening term, $\left( \mathbf{V} \cdot \nabla \right) \mathbf{V}$, determines the rate of steepening of a wave. This can be balanced/offset by loss terms like dispersion (e.g., $\propto \ \beta \ \partial_{x}^{3} v$), diffusion, viscosity (e.g., $\propto \ \nu \ \partial_{x}^{2} v$), resistivity, friction (e.g., $\...


9

Any energy transfer from collisions between the balls won't be transferred faster than light. It will be transferred at the speed of sound within the metal, which is much, much slower than the speed of light. For example, for solid steel balls, the speed of sound is roughly 5900 m/s, so a collision at one end of a 5-cm-long chain of steel balls will take ...


8

How dense is the air in this shockwave...? The density, pressure, temperature, and speed changes across a shock are given by the Rankine-Hugoniot conservation relations. If we use the subscripts $up$ and $dn$ for upstream(pre-shock) and downstream(shocked), respectively, for various parameters then one can show: $$ \frac{ \rho_{dn} }{ \rho_{up} } = \frac{ \...


7

It forms a cone because it depends on a shock wave, and the region enclosed by the shock wave appears conical in shape. See, for example, the apparent cones here: They are also visible here: Wikipedia appears to be fairly clear on why vapor cones are related to shock waves. From the introduction to the article about vapor cones: Atmospheric water then ...


7

You can push the air faster than the speed of sound. If you do that, you will get a shock wave. A shock wave in this sense is a "wall" of supersonic-moving particles. You can definitely achieve this if you push on the air hard enough. A nuclear explosion is definitely "hard enough" :) A shock wave will collide with "normal" stationary air, and give some of ...


7

Well, shock waves are kind of inappropriately named because they do not oscillate, they are actually a discontinuity. A shock wave is the final stage of a nonlinearly steepening wave that has reached a balance between steepening and energy dissipation (i.e., irreversible energy transformation). An contrasting example would be water waves, where there is ...


7

Every object moving through air has a wave front, like a boat moving through water. The faster the object is moving, the larger the wavefront and its amplitude. When two wavefronts run into each other, they add their amplitudes. The wavefronts are slightly behind and to the sides of the fronts of the trains. When two trains pass by each other at high speed, ...


7

If you want to know more about calculating a Mach number, it helps to read Wikipedia's article on Mach number. As explained here, the Mach number for subsonic compressible flow is obtainable from Bernoulli's equation (Wikipedia cites this source). The result you cited then follows from $\gamma=\frac{7}{5},\,p_t=q_e+p$.


7

'Speed of sound' is the maximum rate of propagation of density (or pressure) disturbances in a medium. Imagine some solid body travelling through a fluid at a supersonic speed. As mentioned above, the speed of sound (let's call it $v$) is the maximum rate at which information about density and pressure changes can travel in a fluid. In time $t$, only the ...


6

The first thing that distinguishes a shock wave from an "ordinary" wave is that the initial disturbance in the medium that causes a shock wave is always traveling at a velocity greater than the phase velocity of sound (or light) in the medium. Notice that I said light - that is because there is also a kind of electromagnetic analogue to a shock wave known as ...


6

A pressure wave can travel through solids at a greater speed than through air. And this means a "pre sound" can reach you before the shock wave does - as the motion of the ground will in turn induce a sound wave in the adjacent air.


6

The "commonly held definition" is the wikipedia one... it's not so much a question of distortion, as a question that a wave is symmetrical - that is, it should not result in a net motion of gas. It is possible to construct a sinusoidal pressure wave with a peak pressure of 2 atm and a valley of 0 - from a displacement perspective this is a distorted wave, ...


6

Fracturing of objects is a complex business, but as a general guide yes your teapot is more likely to fracture if it is full of water. The main reason is that shock waves from the impact will be efficiently transmitted through the water. We'll do our usual physicists approximation and consider the teapot as a sphere. Consider what happens when the sphere ...


6

Keeping with the boat wake analogy (which is a good one) you can see the wake from far off, but you cannot "hear" the wake until it reaches you. Your eardrums are like a duck floating on the surface of the lake. When the boat passes by, it is only when the wake passes under the duck that it begins to bob up and down. Since the wake of a boat is in the form ...


5

From my understanding, what's happeneing is the adverse streamwise pressure gradient precludes the boundary layer from progressing downstream past a certain point, and the upstream flow subsequently has nowhere to go but up and off of the body. This is correct, in a sense. The effect of an adverse pressure gradient is to decelerate the flow near the ...


5

my assumption is that I will hear a single note humming in a constant state. A sound wave is not a thing that you can hear. Assume for a moment that you are just standing in the coffee shop, enjoying the music. What you are hearing is not the waves. What you are hearing is the guitar. The waves carry acoustic energy from the guitar to your ear. The ...


5

You can use the ideal gas law here, $$ p=\frac{NkT}{V}=\frac{\rho kT}{\mu m_u} $$ where $\mu$ is the mean molecular weight and $m_u$ the atomic mass unit. You then have a relationship between pressure and temperature: $$ T\sim\frac{p}{\rho} $$ You then have to use an equation of state to relate the energy and pressure, e.g. $$ p=E(\gamma-1) $$ where $\gamma$ ...


5

$M$ is not the speed of sound. It is the Mach number -- the ratio of speed of the aircraft to the speed of sound. The equation is derived from Bernoulli's equation together with a suitable choice of $\gamma=C_P/C_V$ for air.


4

Space isn't empty, as I'm sure you've heard before. There's always something between different bodies, such as the interstellar medium. There are also denser regions of space, including molecular clouds and H I/H II regions. Shockwaves can form in any of these places, and propagate through them. There are several different common sources of these shock waves ...


4

The actual shock wave is quite short lived (I think it's visible for less than a second near 0:14 as a white sheet around the smoke/dust cloud) and doesn't propagate very far in this case. When the shock dissipates what's left is a pressure wave, the "bang" or sonic boom, and that propagates at the speed of sound. So I guess your video uses a reasonable ...


4

The amplitude/intensity of a sonic boom (in Earth's atmosphere) is dependent on the change in pressure across the shock wave. This should make sense, as the intensity of a sound wave is dependent upon its pressure relative to quiet periods. We also know that the ratio of the downstream to upstream pressure is proportional to the square of the Mach number. ...


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