What is Wave?
Wave is a disturbance which carries energy and transfers
from one place to another place. It can be in the form of elastic
deformation, variation of pressure, electric field or magnetic field
intensity etc. A general wave is shown in figure.
Wave Equation:- d2y/dt2 = v2 (d2y/dx2)
Classification of waves
WAVES
MATTER
MEDIUM DIRECTION VIBRATION ENERGY PR
MECHANICAL/ 1D LONGITUDINAL PROGRESSIVE
ELECTRO 2D TRANSVERSE STATIONARY
MAGNETIC 3D
Based on necessity of medium
1. Mechanical Waves
Wave which needs medium to propagate is called a mechanical
wave. The speed of a mechanical wave depends on the elastic and
inertial properties of the medium.
Example- Wave on a string, Sound wave, etc
2. Non-mechanical Waves
Waves which do not need any medium to propagate and can
easily travel through vacuum are termed as Non-mechanical
waves. The speed of these waves in vacuum is a universal
constant that is 299792458 m/s .
Example-Electromagnetic waves, Gravitational Waves.
Electromagnetic waves
In an electromagnetic wave the electric field and magnetic field
oscillate perpendicular to the direction of wave motion. Magnetic
field and electric field are mutually perpendicular.
Examples where electromagnetic wave is involved
Radio and television
Microwaves oven
Radar
Properties of electromagnetic waves
Medium is not required for electromagnetic waves.
They can propagate in the vacuum with the speed of light.
Electromagnetic waves are transverse in nature and can be
polarized.
Electromagnetic waves perform interference and diffraction.
Types of electromagnetic waves
In the increasing order of the wavelength the electromagnetic
waves are
1. Gamma rays : Gamma rays have the wavelength of order 10-
11 m . Used in the medical field. It kills cancer cells.
2. X- rays : X- rays have the wavelength of order 10-9 m and used
to see the inner body part.
3. Ultraviolet : have the wavelength of order 10-7 m , used in
fluorescent tubes. Ultraviolet rays coming from the sun are
harmful for the skin.
4. Visible light : Visible light has the wavelength of order 510-
6 m. It helps in seeing objects of different colors.
5. Infrared : have the wavelength of order 10-5 m. Transfer of
heat from sun, fire and radiators.
6. Microwave : have the wavelength of order 10-3 m . Used in
cooking, radar, telephone and other signals.
7. Radio waves : Radio waves have the wavelength of order
101 m, it is used to broadcast the radio and television.
Matter wave
A french physicist De broglie gave the concept of the dual nature
of matter. According to which, when a matter particle moves with
a larger velocity it behaves as a wave.The wavelength of matter
wave is called de broglie wavelength, and is given by
λ=h/p=h/mv
Where h= planck’s constant = 6.62 × 10-34m2 kg/s
p = momentum of particle
m = mass of particle
v = velocity of particle
However it is difficult to observe this phenomena in day-to -day
life. But it can be seen in various physical experiments like, a
beam of electrons shows diffraction just like the beam of light
which is an electromagnetic wave.
Based on direction of particle motion
1. Transverse wave
Waves in which particles of medium moves perpendicular to the
direction of propagation of waves known as Transverse waves.
Example- Wave on string, Water wave, S-type earthquake wave,
Motion of spring shown in figure.
(a) Velocity of transverse wave,Vt = √T/m = √T/πr2ρ
(b) Vibrations of the particles of medium are normal to
the direction of wave propagation.
2. Longitudinal wave
Waves in which the motion of a particle is along the direction of
propagation of waves is known as longitudinal waves.
Example- Sound wave, P-type earthquake wave, Motion of spring
shown in figure.
Velocity of longitudinal wave, Vl = √E/ρ
(b) Vibrations of the particles are parallel to the direction
of wave propagation.
Based on propagation
1-Dimensional wave
Wave on string is an example of 1-Dimensional wave.
2-Dimensional wave
Water wave is an example of a 2-Dimensional wave.
3-Dimensional wave
Sound Wave is an example of a 3-Dimensional wave.
Properties of Wave
1.Amplitude-
The maximum displacement of an oscillating particle from
mean position is amplitude. Wave transfers the energy and
Amplitude is directly related to energy. Intensity of any wave
is directly proportional to square of amplitude.
2. Wavelength (λ):-
(a) The distance between two crests of successive cycles is
known as Wavelength it is denoted by λ ,since it is length,
its SI unit is (m).
(i) It is defined as the distance travelled by a wave during the
time particle executing SHM completes one vibration.
(ii) It is the distance between two consecutive particles
executing SHM in same phase.
(iii) It is the distance between two consecutive crests or
troughs.
3. Time period-
Time period of a wave is the time taken by the particle of medium
to complete one oscillation denoted by T . It is measured in
seconds.
4. Frequency-
Frequency of wave is the number of oscillations of a particle in a
one second. It is denoted by measured in which is equal to
number of oscillations per second.
Period and frequency are reciprocal of each other .i.e. f=
5. Speed-
speed of wave is actually the measurement of the rate of
propagation of energy in the direction of wave propagation. Speed
of the wave does not depend on the source, it depends on the
inertial and elastic properties of the medium. For a medium
speed of wave is constant.
If λ is the wavelength, T is the time period and f is the frequency
of wave of a wave the speed of wave is v are related as follows:
V= f λ and f=
(6) Wave number (n):- Wave-number of a wave is defined as
the reciprocal of wavelength of weave.
n = 1/λ
Unit of weave number is meter.
(7) Phase:- Phase of a particle is its state which expresses its
position and direction of motion.
(8) Phase difference (Ф):-Phase difference, between two
particles, is the difference between their instantaneous
phases.
Relation between phase difference (Ф) and path difference
(λ):-
phase difference (Ф)= (2π/λ)×(path difference)
Equation of progressive wave:-
A relation between the instantaneous displacement of a
particle executing SHM and time is called equation of
progressive wave.
y = r sin2π (ωt± Ф)
y = r sin [(ωt± (2π/λ)x]
y = r sin (ωt± kx)
y = r sin 2π (t/T ± x/λ)
y = r sin 2π/λ (vt± x)
Angular wave number (k): k = 2π/λ
Relation between particle velocity (V) and wave velocity
(v):-
V = (2πr/λ) vcos[(2π/λ)(vt±x)]
Vmax = (2πr/λ) v
Energy transmission in a progressive wave:-E = ½ mω 2 r 2
Energy per unit volume:- E = ½ ρr 2 ω 2 Here ρ is the density
of medium.
Intensity of a wave:-
I = 2π2ρvf 2r2
Intensity of a wave varies directly as the square of its
amplitude.
So, I ∝ r2
Velocity of transverse wave in stretched string:-
v = √(T/m), Here,T is the tension in the string.
Problems
(1) What is the wavelength of a wave shown in the figure ?
(2).The time period of a wave is 0.2 s, then what is the
frequency of the wave?
(3). An electron is moving with the velocity 1.6 × 106 m/s,
find the wavelength associated with electrons. Mass of an
electron is 9.1 × 10-31 and planck’s constant is 6.62 × 10-
34
m2 kg/s
