Wave Propagation in Discreate Mediums - Help Needed

[sadhu]

i have a doubt in wave propagation in solids
wave propagation i have studied in school is in continuous medium
but real mediums are discreate how will we understnd wave propagation in them
-for wave to transfer from one particle to next takes infinitesimial time but since in continuous medium neighbouring particles are at finite distance the speed
distance/time goes infinite...please help

 

[peeyush_ali]

for a sound wave to travel, the particles of the medium should collide with each other.
In solids, as the relative separation between the molecules is too less than compared to liquids and gases, the differential time interval taken for successive collision is less in solids than in liquids than in gases.So, we can say that sound in solids is more locomotive than in liquids and gases.

 

[Andy Resnick]

i have a doubt in wave propagation in solids
wave propagation i have studied in school is in continuous medium
but real mediums are discreate how will we understnd wave propagation in them
-for wave to transfer from one particle to next takes infinitesimial time but since in continuous medium neighbouring particles are at finite distance the speed
distance/time goes infinite...please help

If the wavelength is much larger than the microstructure of the medium, it is possible to consider the medium as continuous, with perhaps slowly-varying properties. I think this is the essence of the Born approximation, but could not find a pithy website.

 

[sadhu]

i got stuck in this doubt for past four years thinking that in higher classes i might get to know enough to answer the question ..but as you can see i am still in the pipeline..

thanks andy resnick i ,ll google on that..

 

[M Grandin]

Wave propagation speed in a medium is roughly the speed of the molecules in the medium. For instance wave propagation speed in a gas is the speed of molecules in that gas at that temperature. The initial pressure creating the wave just change the speed of molecules slightly and that change is transferred through the medium by molecular collissions. If using a classical view upon it.

In fluids and solids there are of course not free moving molecules as in gases. But there are molecular vibrations that could be ascribed "velocities" corresponding to movements in gases.

 

[sadhu]

what about instantaneous transfer of vibration between neighbouring particles at finite distances making speed infinite(not taking the fact that force spreads with the velocity of light)is continuous medium distance between neighbouring particles is infinitesimial
so is time taken for vibration to spread between two neighbouring particles
hence speed comes finite...

 

[sadhu]

consider three particles A B C
when wave reaches A immidiately(after infinisimial time interval) a force act on B but since in solids the particles are at finite distance the speed which is distance/time must go infinite how does one explain that real mediums act as continuous please help

 

[nnnm4]

It's really no problem. We can solve the equations for N coupled oscillators, and we take the limit that N goes to infinity and the distance between them goes to zero.

 

[sadhu]

ya correct as distance tends to 0 speed acquires a finite value
but wat i am asking is that only continuous medium has infinite oscilators(particles)
wat abt real medium like a crytal which has finite no. of particles at a finite distance
how can it behave like a continuous medium
plx read(ANDY RESNIK) post above to understand wat iam asking

 

[nnnm4]

Well the theory of phonons is how one describes a part of the specific heat capacity of a crystalline solid. The phonons wavelengths are quantized such that nodes and peaks occur at lattice sites.

 

[sadhu]

sorry but i can't figure how phonons are related to the ques. may be because i have yet not studied abt phonons , so let's take sound waves (vibrations) traveling through a metal bock
which is constitued by metal atoms at finite distances ,now can u explain how wave travel
through it by referring wat happen to atoms and if vibrations take infinitesimial time to
jump from one atom to another then speed of wave must be infinite
as distance between atoms in not infinitly small .

 

[nnnm4]

At each lattice site is an atom. These atoms interact with the other atoms at other lattice sites and can be approximated very well as couple harmonic oscillators. By solving these oscillator equations for N oscillators, we gain wave motion.