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v w = λ T size 12{v size 8{w}= { {λ} over {T} } } {}


v w = . size 12{v size 8{w}=fλ} {}

This fundamental relationship holds for all types of waves. For water waves, v w size 12{v rSub { size 8{w} } } {} is the speed of a surface wave; for sound, v w size 12{v rSub { size 8{w} } } {} is the speed of sound; and for visible light, v w size 12{v rSub { size 8{w} } } {} is the speed of light, for example.

Take-home experiment: waves in a bowl

Fill a large bowl or basin with water and wait for the water to settle so there are no ripples. Gently drop a cork into the middle of the bowl. Estimate the wavelength and period of oscillation of the water wave that propagates away from the cork. Remove the cork from the bowl and wait for the water to settle again. Gently drop the cork at a height that is different from the first drop. Does the wavelength depend upon how high above the water the cork is dropped?

Calculate the velocity of wave propagation: gull in the ocean

Calculate the wave velocity of the ocean wave in [link] if the distance between wave crests is 10.0 m and the time for a sea gull to bob up and down is 5.00 s.


We are asked to find v w size 12{v rSub { size 8{w} } } {} . The given information tells us that λ = 10 . 0 m size 12{λ="10" "." 0`"m"} {} and T = 5 . 00 s size 12{T=5 "." "00"`"s"} {} . Therefore, we can use v w = λ T size 12{v size 8{w}= { {λ} over {T} } } {} to find the wave velocity.


  1. Enter the known values into v w = λ T size 12{v size 8{w}= { {λ} over {T} } } {} :
    v w = 10.0 m 5 .00 s . size 12{v size 8{w}= { {"10" "." 0" m"} over {5 "." "00"" s"} } } {}
  2. Solve for v w size 12{v rSub { size 8{w} } } {} to find v w = 2.00 m/s. size 12{v rSub { size 8{w} } } {}


This slow speed seems reasonable for an ocean wave. Note that the wave moves to the right in the figure at this speed, not the varying speed at which the sea gull moves up and down.

Transverse and longitudinal waves

A simple wave consists of a periodic disturbance that propagates from one place to another. The wave in [link] propagates in the horizontal direction while the surface is disturbed in the vertical direction. Such a wave is called a transverse wave    or shear wave; in such a wave, the disturbance is perpendicular to the direction of propagation. In contrast, in a longitudinal wave    or compressional wave, the disturbance is parallel to the direction of propagation. [link] shows an example of a longitudinal wave. The size of the disturbance is its amplitude X and is completely independent of the speed of propagation v w size 12{v rSub { size 8{w} } } {} .

The figure shows a woman holding a long spring in her hand and moving it up and down causing it to move in a zigzag manner away from her. It is an example of a transverse wave, the wave propagates horizontally. The direction of motion of the wave is shown with the help of right arrows at each crest and trough.
In this example of a transverse wave, the wave propagates horizontally, and the disturbance in the cord is in the vertical direction.
The figure shows a woman standing at left pushing a long spring in to and fro motion in horizontal direction away from her without moving her hand up and down. The cord stretches and contracts back and forth. This is an example of a longitudinal wave, the wave propagates horizontally. At some points the spring is compressed and at some other points the spring is expanded. One contracted part is equal to the amplitude X.
In this example of a longitudinal wave, the wave propagates horizontally, and the disturbance in the cord is also in the horizontal direction.

Waves may be transverse, longitudinal, or a combination of the two . (Water waves are actually a combination of transverse and longitudinal. The simplified water wave illustrated in [link] shows no longitudinal motion of the bird.) The waves on the strings of musical instruments are transverse—so are electromagnetic waves, such as visible light.

Sound waves in air and water are longitudinal. Their disturbances are periodic variations in pressure that are transmitted in fluids. Fluids do not have appreciable shear strength, and thus the sound waves in them must be longitudinal or compressional. Sound in solids can be both longitudinal and transverse.

The figure shows a guitar connected to an amplifier and a man holding a sheet of paper facing the speaker attached to the amplifier. The strings of the guitar when played cause transverse waves. On the other hand, the sound of the guitar creates ripples on the sheet of paper causing it to rattle in a direction that shows that the sound waves are longitudinal.
The wave on a guitar string is transverse. The sound wave rattles a sheet of paper in a direction that shows the sound wave is longitudinal.

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, General physics ii phy2202ca. OpenStax CNX. Jul 05, 2013 Download for free at http://legacy.cnx.org/content/col11538/1.2
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