Velocity of mechanical waves

[toam]

Ok, so the velocity of mechanical waves through a medium is equal to the square root of some elastic property divided by some inertial property...

I did a quick search on google and a couple of textbooks and cannot find any actual explanation as to why this is. It is intuitive, yes, but surely there is a decent explanation somewhere?

 

[WhyIsItSo]

Not sure exactly what you want, but for a http://www.physicsclassroom.com/Class/sound/U11L1a.html" description.

If you want http://www.mcasco.com/p1mw.html" .

If you want the http://scienceworld.wolfram.com/physics/WaveVelocity.html" .

If you want to know about http://www.vims.edu/physical/research/TCTutorial/longwaves.htm" , (not tidal), this goes into some description about what the water is actually doing in waves in general, tide waves in particular.

 

[charng]

I can provide a more detailed explanation for the velocity of mechanical waves through a medium. This concept is known as the wave equation, which describes the relationship between the elastic and inertial properties of a medium and the resulting velocity of the waves.

Firstly, let's define the elastic property as the medium's ability to resist deformation and the inertial property as the medium's resistance to changes in motion. These properties are represented by the bulk modulus (K) and density (ρ) of the medium, respectively.

According to the wave equation, the velocity of mechanical waves (v) is equal to the square root of the ratio of the bulk modulus to the density, or v = √(K/ρ). This can also be written as v = √(E/ρ), where E is the Young's modulus of the medium.

This relationship can be understood by considering the behavior of particles in the medium when a wave passes through. As the wave travels, it causes particles in the medium to oscillate around their equilibrium positions. The elastic property of the medium, represented by the bulk modulus, determines how much force is required to displace these particles from their equilibrium positions. The inertial property, represented by the density, determines how quickly the particles can respond to this force and oscillate around their equilibrium positions. Therefore, a higher bulk modulus and/or a lower density will result in a higher velocity of the wave, as the particles can oscillate more quickly and easily.

In summary, the velocity of mechanical waves through a medium is determined by the elastic and inertial properties of the medium, which are represented by the bulk modulus and density, respectively. This relationship is described by the wave equation, v = √(K/ρ) or v = √(E/ρ).