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Longitudinal waves

Longitudinal waves are characterized by the directions of vibration (disturbance) and wave motion. They are along the same direction. It is clear that vibration in the same direction needs to be associated with a “restoring” mechanism in the longitudinal direction.

Consider the case of sound wave. The wave comprises alternating compressions and rarifications. The compressed zone is characterized by higher pressure, which tends to expand the air in the zone. Thus, there is alteration of pressure as the zone transitions from compression to rarification and so on.

It is intuitive to note that all medium types (solid, liquid or gas) support longitudinal waves.

Mathematical description of waves

We shall attempt here to evolve a mathematical model of a traveling transverse wave. For this, we choose a specific set up of string and associated transverse waves traveling through it. The string is tied to a fixed end, while disturbance is imparted at the free end by up and down motion. For our purpose, we consider that pulse is small in dimension; the string is light, elastic and homogeneous. These assumptions are required as we visualize a small traveling pulse which remains undiminished when it moves through the string. We also assume that the string is long enough so that our observation is not subject to pulse reflected at the fixed end.

For understanding purpose, we first consider a single pulse as shown in the figure (irrespective of whether we can realize such pulse in practice or not). Our objective here is to determine the nature of a mathematical description which will enable us to determine displacement (disturbance) of string as pulse passes through it. We visualize two snap shots of the traveling pulse at two close time instants “t” and “t+∆t”. The single pulse is moving towards right in the positive x-direction.

Transverse waves

The vibration and wave motion are at right angle to each other.

Three positions along x-axis named “1”,”2” and “3” are marked with three vertical dotted lines. At either of two instants as shown, the positions of string particles have different displacements from the undisturbed position on horizontal x-axis. We can conclude from this observation that displacement in y-direction is a function of positions of particle in x-direction. As such, the displacement of a particle constituting the string is a function of “x”.

Let us now observe the positions of a given particle, say “1”. It has certain positive displacement at time t = t. At the next snapshot at t=t+∆t, the displacement has reduced to zero. The particle at “2” has maximum displacement at t=t, but the same has reduced at t=t+∆t. The third particle at “3” has certain positive displacement at t=t. At t=t+∆t, it acquires additional positive displacement and reaches the position of maximum displacement. From these observations, we conclude that displacement of a particle at any position along the string is a function of “t”.

Combining two observations, we conclude that displacement of a particle is a function of both position of the particle along the string and time.

Questions & Answers

where we get a research paper on Nano chemistry....?
Maira Reply
nanopartical of organic/inorganic / physical chemistry , pdf / thesis / review
Ali
what are the products of Nano chemistry?
Maira Reply
There are lots of products of nano chemistry... Like nano coatings.....carbon fiber.. And lots of others..
learn
Even nanotechnology is pretty much all about chemistry... Its the chemistry on quantum or atomic level
learn
Google
da
no nanotechnology is also a part of physics and maths it requires angle formulas and some pressure regarding concepts
Bhagvanji
hey
Giriraj
Preparation and Applications of Nanomaterial for Drug Delivery
Hafiz Reply
revolt
da
Application of nanotechnology in medicine
what is variations in raman spectra for nanomaterials
Jyoti Reply
ya I also want to know the raman spectra
Bhagvanji
I only see partial conversation and what's the question here!
Crow Reply
what about nanotechnology for water purification
RAW Reply
please someone correct me if I'm wrong but I think one can use nanoparticles, specially silver nanoparticles for water treatment.
Damian
yes that's correct
Professor
I think
Professor
Nasa has use it in the 60's, copper as water purification in the moon travel.
Alexandre
nanocopper obvius
Alexandre
what is the stm
Brian Reply
is there industrial application of fullrenes. What is the method to prepare fullrene on large scale.?
Rafiq
industrial application...? mmm I think on the medical side as drug carrier, but you should go deeper on your research, I may be wrong
Damian
How we are making nano material?
LITNING Reply
what is a peer
LITNING Reply
What is meant by 'nano scale'?
LITNING Reply
What is STMs full form?
LITNING
scanning tunneling microscope
Sahil
how nano science is used for hydrophobicity
Santosh
Do u think that Graphene and Fullrene fiber can be used to make Air Plane body structure the lightest and strongest. Rafiq
Rafiq
what is differents between GO and RGO?
Mahi
what is simplest way to understand the applications of nano robots used to detect the cancer affected cell of human body.? How this robot is carried to required site of body cell.? what will be the carrier material and how can be detected that correct delivery of drug is done Rafiq
Rafiq
if virus is killing to make ARTIFICIAL DNA OF GRAPHENE FOR KILLED THE VIRUS .THIS IS OUR ASSUMPTION
Anam
analytical skills graphene is prepared to kill any type viruses .
Anam
Any one who tell me about Preparation and application of Nanomaterial for drug Delivery
Hafiz
what is Nano technology ?
Bob Reply
write examples of Nano molecule?
Bob
The nanotechnology is as new science, to scale nanometric
brayan
nanotechnology is the study, desing, synthesis, manipulation and application of materials and functional systems through control of matter at nanoscale
Damian
Is there any normative that regulates the use of silver nanoparticles?
Damian Reply
what king of growth are you checking .?
Renato
What fields keep nano created devices from performing or assimulating ? Magnetic fields ? Are do they assimilate ?
Stoney Reply
why we need to study biomolecules, molecular biology in nanotechnology?
Adin Reply
?
Kyle
yes I'm doing my masters in nanotechnology, we are being studying all these domains as well..
Adin
why?
Adin
what school?
Kyle
biomolecules are e building blocks of every organics and inorganic materials.
Joe
how did you get the value of 2000N.What calculations are needed to arrive at it
Smarajit Reply
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Source:  OpenStax, Oscillation and wave motion. OpenStax CNX. Apr 19, 2008 Download for free at http://cnx.org/content/col10493/1.12
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