Webster's dictionary defines a wave as "a disturbance or

variation that transfers energy progressively from point to

point in a medium and that may take the form of an elastic

deformation or of a variation of pressure, electric or

magnetic intensity, electric potential, or temperature."

http://www.kettering.edu/~drussell/Demos/waves-intro/waves-intro.html

Human wave

© Dan Russell (2002)

http://www.kettering.edu/~drussell/Demos/waves-intro/waves-intro.html

In Longitudinal waves, the particles in a medium oscillate back

and forth about their equilibrium positions but it is the

disturbance which travels, not the individual particles in the

medium.

Longitudinal Wave

© Dan Russell (2002)

http://www.kettering.edu/~drussell/Demos/waves/wavemotion.html

In a transverse wave the particle displacement is

perpendicular to the direction of wave propagation. The

particles do not move along with the wave; they simply

oscillate up and down about their individual equilibrium

positions as the wave passes by.

Transverse wave© Dan Russell (2002)

Water waves are an example of waves that involve a

combination of both longitudinal and transverse motions.

As a wave travels through the water, the particles travel in

circles.

http://www.kettering.edu/~drussell/Demos/waves/wavemotion.html

Water Wave© Dan Russell (2002)

For a sinusoidal plane wave

)cos(),( 0 kxttx

wave theof phase : wave theof amplitude:0

ψ)t-kx(

)(0

)(0

ˆ),(ˆ kxtikxti eetx

Tπ

x T2

constant) fixed, (position 2

To determine angular frequency

To determine wavelength l

l

lπk

tk2

constant) fixed, (time 2

l

disp

lace

men

t()

x

cos( ); a t kx kx

(x,0) (x,Dt)

SB

Time evolution of phase

p

( ) ( ) 0( ) ( )

v

t t k x xt k xxt k

D D D D

D

D

Constant phase surfaces

In three dimension- wave moving in x direction

( , ) cos( )r t A t kx

Wave fronts (constant phase surface)

Phase velocity: vp)cos(),( kxtAtr

Arbitrary direction

Wave vector

Along x

ˆ( , ) cos( . )r t A t k r

:k

Along arbitrary direction

1. LECTURE NOTES FOR PHYSICS ISASTRY AND SARASWAT

2. THE PHYSICS OF VIBRATIONS AND WAVESAUTHOR: H.J. PAINIIT KGP Central LibraryClass no. 530.124 PAI/P