# Tag Info

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The speed of sound in a liquid is given by: $$v = \sqrt{\frac{K}{\rho}}$$ where $K$ is the bulk modulus and $\rho$ is the density. The bulk modulus of mercury is $2.85 \times 10^{10}$ Pa and the density is $13534$ kg/m$^3$, so the equation gives $v = 1451$ m/sec. The speed of sound in solids is given by: $$v = \sqrt{\frac{K + \tfrac{4}{3}G}{\rho}}$$ ...

21

If gas A and gas B are of different density, then the situation sketched is not in equilibrium: the water level on the side of the light gas will be higher. There, the containers are moving down, and you have to push your containers through this net difference in level. You do need to put in energy here, which is probably the piece that you are trying to ...

9

Send an ultrasonic pulse through the gold bar and analyse the returning wave. This technique is actually used to detect impurities in gold bars. To quote this article: Where the wave encounters a region of material with different physical properties – particularly the density and elastic constants – to the rest of the metal, the beam is affected in a ...

8

The answer is No and the reason is the equivalence principle which says that there exist natural units in which the gravitational mass (the mass $m$ in $F=GMm/r^2$) is equal to the inertial mass (the mass $m$ in $F=ma$) for all objects in the Universe. This is equivalent to the statement that all objects, regardless of their composition, density, and other ...

6

Here is a table I made for you listing the elements with a density higher than 10 g/cm$^3$ and their approximate price per kg: I couldn't find any prices for Einsteinium or Actinium and some of the other prices might come from poor sources, but take it as a rough guide. Now you only have to figure out how much you need and your budgetetary constraints, ...

6

The density of mercury (13.534 g/cm^3) does not imply high intermolecular forces. It simply reflects that the mercury atom is much more massive than a water molecule. The atomic weight of mercury is 200.6, while the molecular weight of water is about 18, so mercury atoms take up $\frac {200.6} {18\cdot 13.534}=0.823$ as much volume as a water molecule. ...

6

"The speed of sound is variable and depends on the properties of the substance through which the wave is traveling. In solids, the speed of transverse (or shear) waves depend on the shear deformation under shear stress (called the shear modulus), and the density of the medium. Longitudinal (or compression) waves in solids depend on the same two factors with ...

5

In addition to Bernhard's answer, just because three gases (Gas A,B and air - which is itself a mixture of nitrogen, oxygen, and other gases) have different densities, it does not mean they will remain seperated when in a container. In fact, as entropy of the system increases over time, Gas A, B and air will make an even (if heterogeneous) mixture.

4

If it's a cuboid, then I think a simpler way would be to measure its resistance. Use Suitable contacts Measure resistance Use R=ρL/A and find out resistivity ρ. Either use the table found here and check if it matches up You can also use similar method for other properties like -Thermal conductivity: Heat one end and monitor how quickly the other end's ...

4

I think you're asking if there is some special cutoff density after which spacetime "collapses" and forms a black hole. If this is your question then the answer is no, there is no specific cutoff. Density unites are $\frac{\mathrm{mass}}{\mathrm{volume}}$ but the size of black holes is dependent on the mass and the size is not proportional to the volume ...

4

As @Qmechanic points out in his answer, making the substitution $z \rightarrow z - r$ (going from the first version to the second in the identity) works. That's the math answer. The physical intuition is that, in order for the system to have perfect cylindrical symmetry, it must extend to $z = \pm \infty$. That corresponds to integrating your $z$ variable ...

4

John Rennie has provided an exact mathematical treatment of the equations behind the calculation of the speed of sound. I don't want to detract from that treatment, and of course the Wikipedia articles we both draw from provide a broader treatment; but an intuitive understanding of the 'why' has been equally helpful for me, in the past. The following is my ...

3

It does not work for the following reason. Let's look at the right side, where the containers float to the top. When a new container enters at the bottom (from water to gas B), it pushes some gas B away, so it can occupy the space. The pushed away gas B has nowhere to go, but up. Gaining height means potential energy. That is energy used, to make the ...

3

I don't think that this question is still fully resolved, water is a fascinating molecule! But here are some thoughts. Clearly, if ice is lighter than liquid water it is because it doesn't pack as well. Its an example of how a random-ish packing can be more efficient than an ordered packing of a "weirdly" shaped molecule. Imagine throwing LEGOs into a box, ...

3

I don't think the term electron probability cloud has a precisely defined meaning. It's more of a metaphor meant to show that the electron does not have a well defined position. Like any quantum particle the electron does not have a position until you interact with it e.g. scatter another particle off it. The interaction takes place around some position (I ...

3

Different objects with the same mass but different sizes will have different gravitational pulls at their surface, which is probably what you heard. But that is only because their surfaces are in different places. If you compare the gravitational pulls of different objects with the same mass at a fixed distance away from their centers, you will find that ...

3

This is really a footnote to Carl's answer: As Carl explains, in Mathematics we approach the zero volume/infinite density as a limit and this is a perfectly well defined process. However in Physics we generally don't believe that infinite quantities exist and the occurrence of an infinity is usually a sign that our theory needs modification. In the case of ...

3

NaCl melts at around 800°C. Molten NaCl has a density of about $1.556 \frac{g}{cm^3}$[1], at room temperature (solid) it has one of $2.71\frac{g}{cm^3}$ [2]. Sadly I could not find a value for the density at barely underneath melting point but I strongly assume that the density is a strictly monotonously falling function of temperature. Therefore solid NaCl ...

3

The square of the sound velocity is proportional to the ratio of an elastic modulus to the mass density of the material.The reason why the sound velocity is usually larger in solids than in liquids and usually larger in liquids than in gases is because of the elastics constants of the material. What determines the elastic constants of a material is the ...

2

This is a great question, although unfortunately it turns out to be very difficult to interpret it in a way that allows a definite answer. The question is ambiguous because of the way mass is defined in relativity. From the way the question is posed, I assume the OP doesn't have a lot of technical background in relativity. However, there is no way to resolve ...

2

You can take a Reissner-Nordström solution for the charged non-rotating black hole, and put its mass $m=0$. Then it would become a so-called naked singularity. More precisely, singularity is a point where some value ends at infinity, while density of mass being just one option. For more thorough consideration of Reissner-Nordstrom and Kerr-Newman solutions, ...

2

The laws of physics are local so if you change something on one side of your celestial body, it won't immediately affect other parts of the celestial body. In fact, your friend won't experience anything special even after the signals about the turning on of your machine get to your friend. He will just find himself on the surface of a collapsing neutron star ...

2

Uniform acceleration is not realistic in this problem. Why even include the text about the expansion of the balloon, if it is not going to be taken into account? The only way the balloon could continuously accelerate would be if it experiences no drag from the water. But even if we go with this greatly simplifying assumption, it is still far, far from ...

2

I just read that statement from Wikipedia, and when they were mathematically calculating the density, they were using the Schwarzschild radius (aka radius of event horizon), not the singularity. The singularity itself, theoretically, has infinite density and exists in one point (radius approaches 0), so no, it won't float on water. Always remember when the ...

2

Multidimensional Dirac delta is usually defined as $$\delta_{3D}(x,y,z)=\delta(x)\delta(y)\delta(z)$$ You can find its Fourier transform as a convolution of constants, which will still appear constant. Alternatively, you can just use the definition and find triple integral, which will give the same result: ...

2

$$\rho=\frac{n*M}{V}$$ With $n$ the number of moles of the gas, $M$ the molar mass of the gas, and $V$ the volume of the gas. $n$ and $M$ are constant, so: $$\rho_1=\rho_0*\frac{V_0}{V_1}$$ For $V$ we have: $$V=\frac{n r T}{p}$$ $n$ and $R$ are constant, so: $$V_1=V_0*\frac{T_1}{T_0}*\frac{p_0}{p_1}$$ So: $$\rho_1=\rho_0*\frac{T_0}{T_1}*\frac{p_1}{p_0}$$ ...

2

Wikipedia quotes Other substances that expand on freezing are silicon, gallium, germanium, antimony, bismuth, plutonium and also chemical compounds that form spacious crystal lattices with tetrahedral coordination. EDIT:The same paragraph says silicon dioxide also exhibits this property.

2

The following relation describes the total electric flux density in a medium: In the previous equation, D is the total electric flux density, epsilon is the free space permittivity . E is the external applied electric field, and P is the polarization vector. The polarization vector represents the reaction of the medium to the externally applied electric ...

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