Speed of a Wave vs. Density of a Medium

In summary, the question is if sound waves travel faster in more dense or less dense mediums. The answer is that it depends on the type of wave and the way it is transmitted. For an ideal gas, the speed of sound is dependent on pressure and density, so increasing pressure while holding temperature constant will not change the speed. In general, the speed of sound in fluids is determined by the bulk modulus, which means that increasing density in a liquid will increase the speed. In contrast, light does slow down as it passes into a more dense medium.
  • #1
jumbogala
423
4

Homework Statement


Hi everyone. I watched a YouTube video earlier today which said that sound waves travel faster in more dense mediums. For example, sound travels faster in water than it does in air.

However, on this webpage http://www.physicsclassroom.com/mmedia/waves/ltm.cfm it says that "the wave speed is always greatest in the least dense medium".

So which is true?

Homework Equations

The Attempt at a Solution


I am thinking that maybe it depends on the type of wave, and that transmitted/reflected waves work differently than sound waves.
 
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  • #2
As I understand it (not an expert though) it depends what you mean by going to a denser medium.
Increasing the mass of the individual particles (gas molecules, atoms in a solid lattice..) will reduce the speed.
Packing the particles closer or increasing their repulsion may increase the speed.
For an ideal gas, the speed is ##\sqrt{\frac{\gamma p}{\rho}}##, where p is pressure and rho is density, so increasing pressure but holding temperature constant should not make any difference. The higher pressure balances the increased density.
For a fluid in general it is ##\sqrt{\frac{K}{\rho}}##, where K is the bulk modulus. For the gas case, that reduces to the same as above, but liquids have a much higher bulk modulus than gases (more than the relative increase in density), so going from gas to liquid tends to increase the speed.
The speed of sound in water reaches a maximum at about 70C, then declines a little.
 
  • #3
In a gas the speed of sound depends on the mass of the molecules (∝√1/m)) and on the absolute temperature (∝√T) so for any particular gas the only major effect is Temperature. Sound is transmitted by translational movement of molecules. (density has little influence)
In liquids and solids sound is transmitted by vibrational motion of molecules and the elastic properties of the solid or liquid are the major influence on the speed.
Light, of course, does slow down as it passes into the more dense medium and a phase change occurs in any reflection from less dense to more dense medium. This is noted in the 'physics classroom' site that you mentioned.
 

1. What is the relationship between the speed of a wave and the density of the medium it travels through?

The speed of a wave is directly proportional to the square root of the density of the medium it travels through. This means that as the density of the medium increases, the speed of the wave also increases.

2. How does the density of a medium affect the wavelength of a wave?

The density of a medium does not directly affect the wavelength of a wave. However, the speed of the wave is affected by the density, which in turn can affect the wavelength through the equation v = fλ, where v is the speed, f is the frequency, and λ is the wavelength.

3. Does the speed of a wave change when it travels through different materials with varying densities?

Yes, the speed of a wave will change when it travels through different materials with varying densities. The denser the medium, the faster the wave will travel.

4. Is the density of a medium the only factor that affects the speed of a wave?

No, the speed of a wave is also affected by other factors such as the temperature, pressure, and elasticity of the medium. These factors can alter the density of the medium, thus indirectly affecting the speed of the wave.

5. How does the density of a medium affect the amplitude of a wave?

The density of a medium does not directly affect the amplitude of a wave. However, the speed of the wave is affected by the density, which in turn can affect the amplitude through the equation v = √(T/μ), where T is the tension of the medium and μ is the linear density. Higher density results in a higher speed and thus a higher amplitude for a given tension and linear density.

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