Wave
Introduction:
Let us consider the situation, where two men are standing on the two shores of the river. In how
many ways they can communicate with each other? For example one can shout. Another method
is to use the flash light. One more is to through stone or arrow towards that man or drop stone in
water very near to that man. Basically most of these ways have something common that is
production of wave or wave motion.
Most information about our surrounding comes to us in some form of wave. Sound comes to our
ears, light to our eyes, electromagnetic signals to radio, mobilesand television sets all these are
possible due to wave motion.
What are waves?
A still pond of water has calm surface. When we drop a stone in still pond, we see some
movement on thesurface of water.It generates ripples on the water surface and the ripples slowly
spread out. A tranquil leaf floating at some point starts oscillating up and down.
A still pond has not remained that still now. Water surface starts oscillating with some
energy.The stone had some kinetic energy. When it strikes the calmwater surface, some of its
energy is used to generate and spread ripples on water surface in all possible directions. These
ripples will eventually be circular and reach to thefloatingleaf. It causes the leaf to move up and
down.The leaf has acquired some energy that was originally possessed by the stone.The energy
has been transmitted from the place wherestone entered the pond to the place of leaf.The
particles on the surface of water oscillate at their own position, they do not leave their place but
the energy gets transmitted via disturbance. Such oscillatory disturbance, which causes
transmission of the energy from one point to another, is known as Wave.
So, waves can be viewed as entity that transfers energy rather than the movement of particles.
Particles of the medium participate in wave formation but they are not the wave. Let us consider
the case of water waves.
Waveon water consists of peaks & troughs. A peak (or crest) is place where water rises higher
and at troughwater sinks lower than the water level when it was still.
Characteristics of waves:
1) Amplitude:
The characteristic height of the peak or the
depth of the trough is known as amplitude.
Normally letter A is used for amplitude. The
unit of amplitude is the unit of length, so SI
unit of amplitude is meter (m).
Amplitude is the maximum displacement of particle from mean position.
2) Wavelength:
Let us look at the distance between adjacent peaks of the wave. The distance is same no
matter which two peaks we choose. Let us look at the
distance between two adjacent troughs. Here also the
distance is same no matter which two troughs we
select. But more importantly it is same as the distance
between two adjacent peaks. This distance which is
characteristic of the wave is known as the
wavelength. The symbol for wavelength is. The unit is again of length. So unit of
wavelength meter (m).
The wavelength is the distance between any two successive points on wave which are in
phase. They don’t have to be peaks or troughs.
3) Period:
Let us again consider the case of water waves. Let us focus on one particular point. From
that point first one peak goes then one trough & then again the peak goes. We can
measure the timebetween two adjacent peaks or troughs. The time we have measured is
the time for one wavelength to pass by. This time is known as period of the wave. T is the
symbol used to denote period of wave & the unitissecond (s).
Period is the time required to complete one oscillation of the vibrating source or period
is time required for one wavelength or two successive crests to cross the reference points.
4) Frequency:
There is another way of characterizing the period of the wave. We have measured the
time for one wavelength to pass a fixed point. We can turn this around and say how many
waves pass by a fixed point in one second. This term is known as frequency of the
wave.It is denoted by f or n.The unit of frequency is Hertz (Hz).
Frequency of the wave is the number of oscillations performed by the vibrating particle
per second or frequency is number of wavelengths crossing the reference point in one
second.
5) Wave speed:
Speed is the distance travelled divided by the time required to cover that distance. This
will help us, because we know that the wave travels wavelength  in time T. From this
we can calculate the speed of the wave.
The relation between velocity & wavelength of the wave can also be written as below:
This relation is known as wave equation. This relationship holds true for all kinds of
waves like sound wave & light wave.
From Activity1, we can say that the speed of wave changes if medium is changed.
Velocity of given type of wave in a given medium has a unique value.Under same
physical conditions for all frequencies in a given medium velocity /speed remains same.
6) Phase :
Phase is state of motion. It is measured in terms
angle. The waves in diagram a) are said to be in
phase. The waves in diagram b) are said to be out
phase.
Types of waves:
1) Mechanical wave:
Mechanical wave needs the medium to travel. The particle of the medium does not move
from its initial position. It oscillates about mean initial position. By such oscillationsthe
energy is transferred to the connected neighboring particle. A mechanical wave requires
aninitial energy input. Once the energy is added, the wave travels till all energy
istransferred.Some energy gets absorbed in the medium during process of wave motion.
Ocean waves & sound waves are mechanical waves.
2) Electromagnetic wave:
Electromagnetic waves are those waves which do not need any medium at all to
propagate from one place to another. They are capable of transmitting energy through
vacuum. Light waves are electromagnetic waves.
Waveforms:
1) Longitudinal wave:
Wave in which the particles of the medium vibrate about their mean
position in a parallel or antiparallel way to the direction of propagation
of the wave is defined as the longitudinal wave. The longitudinal wave
can be demonstrated by giving impulse to stretch slinkyas shown in
the figure. (Slinky is the helical spring. It can be stretched.) In this
figure, we see that disturbance travels in same direction as that of
wave. Part of slinky compressed, when we push it. Part of slinky is
stretched, when we pull it. Compressed region is known as
compression and stretched region is known as rarefaction. Both
compressions and rarefactions travel in same direction along the
slinky.
The wavelength of the longitudinal wave is the distance between two successive compressions or
two successive rarefactions. The most common example of longitudinal wave is sound wave.
Another example of the longitudinal wave is movement of grass in grass land. The grass
movesas wind passes through it. If we see grass from elevated position, we can see waves
travelling across the grass land. The individual stems of grass do not leave the place; instead they
swing to and fro about their mean position.
2) Transverse Wave:
Wave in which the particles of the medium vibrate about their mean
position in a direction perpendicular to the direction of propagation of
the wave is known as Transverse wave.
This can be demonstrated by stretched string. If stretched string is plucked, a wave passes over it.
All points on the string move up & down as wave pulse pass along the length of the string.Some
examples of transverse waves are light waves, water wave on the surface.
Properties of waves:
All types of waves exhibit the phenomenon of reflection, refraction, interference and diffraction.
These phenomenon play important role in both hearing and seeing.
1) Reflection:
When an object, like a ball, is thrown against a rigid wall it bounces back. This "reflection" of
the object can be analyzed by applying universal principles of momentum and energy
conservation. If the collision between ball and wall is perfectly elastic, then all the incident
energy and momentum is reflected, and the ball bounces back with the same speed. If the
collision is inelastic, then the wall (or ball) absorbs some of the incident energy and momentum.
In this case the ball does not bounce back with the same speed.
Waves also carry energy & momentum. Whenever waves encounter an obstacle, they are
reflected back. This reflection depends upon nature of the obstacle. The reflection of waves is
responsible for echo& importantly for the production of standing
waves. These standing waves play very important role in musical
instruments.
Reflected waves have certain properties.If the wave hits the
surface at right angle the wave reflect backwards as shown in the
diagram.
If the wave strikes the obstacle at some angle then it does not reflect
backwards.Direction of propagation of wave is known as ray. The
angle made by the incident ray with normal is incident angle &
denoted by i. The angle made by the reflected ray with normal is
reflected angle(r). As shown in the figure. We can measure these
angles.
The law of reflection states that the angle of incidence is equal to the angle of reflection.
2) Refraction:
Sometimes wave moves from one medium to another. As we have seen in activity 1, velocity of
the wave is the property of the medium. As the medium is changed velocity also changes. We
know ‘v = f’, if velocity changes, the multiplication of ‘f’ and ‘’ must change. But the
frequency does not change so wavelength changes.That is the distance covered by the wave in
unit time changes.
The refraction is surface phenomenon. It takes place at the boundary between two different
media. Refraction happens due to change in wave speed as medium is changed, but frequency
remains unchanged. So the refraction of the wave is change in the direction of wave due to
change in its speed.
Refraction of light is most commonly observed phenomenon but all other waves refract when
they pass from one medium to another. For example when sound waves pass from one medium
to another, it also refracts.
3) Interference:
Whentwo waves meet, interesting things can happen. Waves are
basically collective motion of the particles. When two waves meet,
both of them try to impose their motion on particles. The result of
this is the Interference pattern.
Principle of superposition:
When two or more waves arrive at a point simultaneously, the
displacement of the particle produced by each wave is independent
of another wave. The net displacement of particle is vector sum of
the individual displacements produced by each wave independently.
See the diagram.
Interference is based on the Principle of Superposition. It is the
phenomenon in which two waves superimpose over each other to
form a complex wave of greater or lower amplitude.
4) Diffraction:
We know that the ray travels in straight line in a uniform medium but commonly changes the
direction when medium is changed. But there is one more important property of the wave that
isknown as diffraction.
Let us consider the situation of shadow formation of solid object. The shadow region of the
object must be dark and we must see the sharp edges at the boundary of shadow. But this is not
case. The boundaries are not sharp, they are fuzzy. That is by some way light reaches in the
region where it is not expected.Now consider the slit in place of the edge of the solid object. We
will place light source at one side & screen at another. The slit has two edges. So we expect a
bright band of specific width on the screen. But again this is not the case. The width is larger
than expectation & boundaries are fuzzy. These situations can be explained only by the
Diffraction phenomenon.
In very simple words, it can be explained as ‘Diffraction is the phenomenon of bending of wave
at the edge’.
We can see this pattern by small activity. Stretch fingers of your palm & hold it against light
source. Now try to form slit in between any two fingers by slightly moving one finger. You can
observe bright & dark fringes formed due to that slit. This is thediffraction pattern.
5) Polarization:
Polarization is property of wave, all waves cannot be polarized. Only Transverse waves can be
polarized.
While thinking of Polarization, we need to visualize a transverse wave in three dimensions. We
know that light wave is an electromagnetic & transverse wave. It can be polarized. We will see
the details while learning Light.
When the oscillations of a wave are constrained in only one direction or plane, such wave is
known astotally Polarized wave & the phenomenon is known as Polarization.