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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

Is there any normative that regulates the use of silver nanoparticles?
Damian Reply
what king of growth are you checking .?
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
yes I'm doing my masters in nanotechnology, we are being studying all these domains as well..
what school?
biomolecules are e building blocks of every organics and inorganic materials.
anyone know any internet site where one can find nanotechnology papers?
Damian Reply
sciencedirect big data base
Introduction about quantum dots in nanotechnology
Praveena Reply
what does nano mean?
Anassong Reply
nano basically means 10^(-9). nanometer is a unit to measure length.
do you think it's worthwhile in the long term to study the effects and possibilities of nanotechnology on viral treatment?
Damian Reply
absolutely yes
how to know photocatalytic properties of tio2 nanoparticles...what to do now
Akash Reply
it is a goid question and i want to know the answer as well
characteristics of micro business
for teaching engĺish at school how nano technology help us
Do somebody tell me a best nano engineering book for beginners?
s. Reply
there is no specific books for beginners but there is book called principle of nanotechnology
what is fullerene does it is used to make bukky balls
Devang Reply
are you nano engineer ?
fullerene is a bucky ball aka Carbon 60 molecule. It was name by the architect Fuller. He design the geodesic dome. it resembles a soccer ball.
what is the actual application of fullerenes nowadays?
That is a great question Damian. best way to answer that question is to Google it. there are hundreds of applications for buck minister fullerenes, from medical to aerospace. you can also find plenty of research papers that will give you great detail on the potential applications of fullerenes.
what is the Synthesis, properties,and applications of carbon nano chemistry
Abhijith Reply
Mostly, they use nano carbon for electronics and for materials to be strengthened.
is Bucky paper clear?
carbon nanotubes has various application in fuel cells membrane, current research on cancer drug,and in electronics MEMS and NEMS etc
so some one know about replacing silicon atom with phosphorous in semiconductors device?
s. Reply
Yeah, it is a pain to say the least. You basically have to heat the substarte up to around 1000 degrees celcius then pass phosphene gas over top of it, which is explosive and toxic by the way, under very low pressure.
Do you know which machine is used to that process?
how to fabricate graphene ink ?
for screen printed electrodes ?
What is lattice structure?
s. Reply
of graphene you mean?
or in general
in general
Graphene has a hexagonal structure
On having this app for quite a bit time, Haven't realised there's a chat room in it.
what is biological synthesis of nanoparticles
Sanket Reply
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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