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We then have an alternate definition of the wavelength as the distance between any two adjacent points which are in phase .

Wavelength of wave

The wavelength of a wave is the distance between any two adjacent points that are in phase.

Points that are not in phase, those that are not separated by a complete number of wavelengths, are called out of phase . Examples of points like these would be A and C , or D and E , or B and H in the Activity.

Period and frequency

Imagine you are sitting next to a pond and you watch the waves going past you. First one peak arrives, then a trough, and then another peak. Suppose you measure the time taken between one peak arriving and then the next. This time will be the same for any two successive peaks passing you. We call thistime the period , and it is a characteristic of the wave.

The symbol T is used to represent the period. The period is measured in seconds ( s ).

Period ( T )
The period ( T ) is the time taken for two successive peaks (or troughs) to pass a fixed point.

Imagine the pond again. Just as a peak passes you, you start your stopwatch and count each peak going past. After 1 second you stop the clock and stop counting. The number of peaks that you have counted in the 1 second is the frequency of the wave.

Frequency
The frequency is the number of successive peaks (or troughs) passing a given point in 1 second.

The frequency and the period are related to each other. As the period is the time taken for 1 peak to pass, then the number of peaks passing the point in 1 second is 1 T . But this is the frequency. So

f = 1 T

or alternatively,

T = 1 f

For example, if the time between two consecutive peaks passing a fixed point is 1 2 s , then the period of the wave is 1 2 s . Therefore, the frequency of the wave is:

f = 1 T = 1 1 2 s = 2 s - 1

The unit of frequency is the Hertz ( Hz ) or s - 1 .

What is the period of a wave of frequency 10 Hz ?

  1. We are required to calculate the period of a 10 Hz wave.

  2. We know that:

    T = 1 f
  3. T = 1 f = 1 10 Hz = 0 , 1 s
  4. The period of a 10 Hz wave is 0,1 s .

Speed of a transverse wave

In Motion in One Dimension , we saw that speed was defined as

speed = distance traveled time taken

The distance between two successive peaks is 1 wavelength, λ . Thus in a time of 1 period, the wave will travel 1 wavelength in distance. Thus the speed of the wave, v , is:

v = distance traveled time taken = λ T

However, f = 1 T . Therefore, we can also write:

v = λ T = λ · 1 T = λ · f

We call this equation the wave equation . To summarise, we have that v = λ · f where

  • v = speed in m · s - 1
  • λ = wavelength in m
  • f = frequency in Hz

When a particular string is vibrated at a frequency of 10 Hz , a transverse wave of wavelength 0,25 m is produced. Determine the speed of the wave as it travels along the string.

    • frequency of wave: f = 10 Hz
    • wavelength of wave: λ = 0,25 m

    We are required to calculate the speed of the wave as it travels along the string. All quantities are in SI units.

  1. We know that the speed of a wave is:

    v = f · λ

    and we are given all the necessary quantities.

  2. v = f · λ = ( 10 Hz ) ( 0 , 25 m ) = 2 , 5 m · s - 1
  3. The wave travels at 2,5 m · s - 1 along the string.

Questions & Answers

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
anyone know any internet site where one can find nanotechnology papers?
Damian Reply
research.net
kanaga
sciencedirect big data base
Ernesto
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.
Bharti
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
Daniel
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
Maciej
characteristics of micro business
Abigail
for teaching engĺish at school how nano technology help us
Anassong
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
NANO
what is fullerene does it is used to make bukky balls
Devang Reply
are you nano engineer ?
s.
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.
Tarell
what is the actual application of fullerenes nowadays?
Damian
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.
Tarell
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.
Virgil
is Bucky paper clear?
CYNTHIA
carbon nanotubes has various application in fuel cells membrane, current research on cancer drug,and in electronics MEMS and NEMS etc
NANO
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.
Harper
Do you know which machine is used to that process?
s.
how to fabricate graphene ink ?
SUYASH Reply
for screen printed electrodes ?
SUYASH
What is lattice structure?
s. Reply
of graphene you mean?
Ebrahim
or in general
Ebrahim
in general
s.
Graphene has a hexagonal structure
tahir
On having this app for quite a bit time, Haven't realised there's a chat room in it.
Cied
what is biological synthesis of nanoparticles
Sanket Reply
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Source:  OpenStax, Physics - grade 10 [caps 2011]. OpenStax CNX. Jun 14, 2011 Download for free at http://cnx.org/content/col11298/1.3
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