# 0.1 Transverse waves  (Page 3/4)

 Page 3 / 4

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 this time 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 ( $\mathrm{s}$ ).

Period ( $\mathrm{T}$ )
The period ( $\mathrm{T}$ ) 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 $\frac{1}{T}$ . But this is the frequency. So

$f=\frac{1}{T}$

or alternatively,

$T=\frac{1}{f}$

For example, if the time between two consecutive peaks passing a fixed point is $\frac{1}{2}\phantom{\rule{0.166667em}{0ex}}\mathrm{s}$ , then the period of the wave is $\frac{1}{2}\phantom{\rule{0.166667em}{0ex}}\mathrm{s}$ . Therefore, the frequency of the wave is:

$\begin{array}{ccc}\hfill f& =& \frac{1}{T}\hfill \\ & =& \frac{1}{\frac{1}{2}\phantom{\rule{0.166667em}{0ex}}\mathrm{s}}\hfill \\ & =& 2\phantom{\rule{0.166667em}{0ex}}{\mathrm{s}}^{-1}\hfill \end{array}$

The unit of frequency is the Hertz ( $\mathrm{Hz}$ ) or ${\mathrm{s}}^{-1}$ .

What is the period of a wave of frequency $10\phantom{\rule{2pt}{0ex}}\mathrm{Hz}$ ?

1. We are required to calculate the period of a $10\phantom{\rule{2pt}{0ex}}\mathrm{Hz}$ wave.

2. We know that:

$T=\frac{1}{f}$
3. $\begin{array}{ccc}\hfill T& =& \frac{1}{f}\hfill \\ & =& \frac{1}{10\phantom{\rule{0.166667em}{0ex}}\mathrm{Hz}}\hfill \\ & =& 0,1\phantom{\rule{0.166667em}{0ex}}\mathrm{s}\hfill \end{array}$
4. The period of a $10\phantom{\rule{2pt}{0ex}}\mathrm{Hz}$ wave is $0,1\phantom{\rule{2pt}{0ex}}\mathrm{s}$ .

## Speed of a transverse wave

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

$\mathrm{speed}=\frac{\mathrm{distance}\phantom{\rule{2pt}{0ex}}\mathrm{traveled}}{\mathrm{time}\phantom{\rule{2pt}{0ex}}\mathrm{taken}}$

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

$v=\frac{\text{distance}\phantom{\rule{4.pt}{0ex}}\text{traveled}}{\text{time}\phantom{\rule{4.pt}{0ex}}\text{taken}}=\frac{\lambda }{T}$

However, $f=\frac{1}{T}$ . Therefore, we can also write:

$\begin{array}{ccc}\hfill v& =& \frac{\lambda }{T}\hfill \\ & =& \lambda ·\frac{1}{T}\hfill \\ & =& \lambda ·f\hfill \end{array}$

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

• $v=$ speed in $\mathrm{m}·\mathrm{s}{}^{-1}$
• $\lambda =$ wavelength in $\mathrm{m}$
• $f=$ frequency in $\mathrm{Hz}$

When a particular string is vibrated at a frequency of $10\phantom{\rule{2pt}{0ex}}\mathrm{Hz}$ , a transverse wave of wavelength $0,25\phantom{\rule{2pt}{0ex}}\mathrm{m}$ is produced. Determine the speed of the wave as it travels along the string.

• frequency of wave: $f=10\mathrm{Hz}$
• wavelength of wave: $\lambda =0,25\mathrm{m}$

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:

$v=f·\lambda$

and we are given all the necessary quantities.

2. $\begin{array}{ccc}\hfill v& =& f·\lambda \hfill \\ & =& \left(10\phantom{\rule{0.277778em}{0ex}}\mathrm{Hz}\right)\left(0,25\phantom{\rule{0.166667em}{0ex}}\mathrm{m}\right)\hfill \\ & =& 2,5\phantom{\rule{0.166667em}{0ex}}\mathrm{m}·{\mathrm{s}}^{-1}\hfill \end{array}$
3. The wave travels at $2,5\phantom{\rule{2pt}{0ex}}\mathrm{m}·\mathrm{s}{}^{-1}$ along the string.

where we get a research paper on Nano chemistry....?
nanopartical of organic/inorganic / physical chemistry , pdf / thesis / review
Ali
what are the products of Nano chemistry?
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
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
revolt
da
Application of nanotechnology in medicine
what is variations in raman spectra for nanomaterials
ya I also want to know the raman spectra
Bhagvanji
I only see partial conversation and what's the question here!
what about nanotechnology for water purification
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
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?
what is a peer
What is meant by 'nano scale'?
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 ?
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?
what king of growth are you checking .?
Renato
What fields keep nano created devices from performing or assimulating ? Magnetic fields ? Are do they assimilate ?
why we need to study biomolecules, molecular biology in nanotechnology?
?
Kyle
yes I'm doing my masters in nanotechnology, we are being studying all these domains as well..
why?
what school?
Kyle
biomolecules are e building blocks of every organics and inorganic materials.
Joe
The fundamental frequency of a sonometer wire streached by a load of relative density 's'are n¹ and n² when the load is in air and completly immersed in water respectively then the lation n²/na is
Properties of longitudinal waves