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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.

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

what is variations in raman spectra for nanomaterials
Jyoti Reply
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.
yes that's correct
I think
what is the stm
Brian Reply
is there industrial application of fullrenes. What is the method to prepare fullrene on large scale.?
industrial application...? mmm I think on the medical side as drug carrier, but you should go deeper on your research, I may be wrong
How we are making nano material?
what is a peer
What is meant by 'nano scale'?
What is STMs full form?
scanning tunneling microscope
how nano science is used for hydrophobicity
Do u think that Graphene and Fullrene fiber can be used to make Air Plane body structure the lightest and strongest. Rafiq
what is differents between GO and RGO?
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
what is Nano technology ?
Bob Reply
write examples of Nano molecule?
The nanotechnology is as new science, to scale nanometric
nanotechnology is the study, desing, synthesis, manipulation and application of materials and functional systems through control of matter at nanoscale
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 did you get the value of 2000N.What calculations are needed to arrive at it
Smarajit 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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