1) Waves transfer energy through a medium from one point to another without the medium itself traveling. 2) There are two main types of mechanical waves - transverse waves, where the vibration is perpendicular to the direction of travel, and longitudinal waves, where the vibration is parallel. 3) When two waves interact according to the principle of superposition, their individual displacements are summed at any given point. This can result in interference patterns with amplitudes that are enhanced or reduced.

1. Waves
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Waves- By Aditya Abeysinghe
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2. A wave allows energy to be transferred from one point to
another some distance away without any particles of the
medium travelling between the two points.
E.g.:
Waves- By Aditya Abeysinghe
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3. Characteristics of a wave
Let’s take a simple example.
Displacement
Crest
Wave length (λ)
amplitude
Distance
Trough
You may have seen that there is a repetition of the shape and the
position of particles over a certain distance.
Waves- By Aditya Abeysinghe
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4. The distance between two such particles are to be
said be in the same phase and the distance
between these two particles is called the wave
length. The maximum height achieved from the
median position is called the amplitude of the wave.
Thus, the distance between corresponding points in
successive waveforms, such as two successive
crests or twosuccessive troughs , is called the
wavelength, λ.
Within a single vibration of this wave, the waveform
moves a distance λ.
Waves- By Aditya Abeysinghe
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5. So, in one second, when f vibrations occur,
the waveform moves a distance fλ. So, the
distance travelled in unit time is fλ
However, by the definition of speed,
Speed = distance travelled in unit time.
So, the speed of the wave = fλ
Therefore, V = fλ
This relationship between V, f and λ is true for
any type of wave , i.e. mechanical, sound or
electromagnetic.
Waves- By Aditya Abeysinghe
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6. Types of waves
There are various types of waves. Some types are
visible while others are invisible. Some waves are
tangible while others are intangible.
However, in this presentation I have focussed only
on the mechanical waves. Mechanical waves, like
sound waves, need a medium of propagation.
Depending on the characteristics of waves,
mechanical waves can mainly be divided to two
types as :
1. Transverse waves
2. Longitudinal waves
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7. Transverse waves
A wave which is propagated by vibrations perpendicular to the
direction of travel of the wave is called a transverse wave.
Some of the examples of transverse waves are:
Waves- By Aditya Abeysinghe
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8. The propagation of a transverse wave can be illustrated as
follows:
Displacement
Distance
Trough
Waves- By Aditya Abeysinghe
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9. Longitudinal Waves
A longitudinal wave is a wave in which the vibrations occur in
the same direction as the direction of travel of the wave.
Some of the examples of longitudinal waves are:
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10. The propagation of a longitudinal wave can be illustrated as
follows:
Rarefaction
Compression
Rarefaction
Compression
Rarefaction
distance
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11. Progressive waves
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Progressive waves are the waves in which particles travel
along with the speed of the wave. As opposed to progressive
waves, stationary waves (which will be described later in this
presentation) also move along the speed of the wave.
However, in a stationary wave, the waveform is reflected back
along the direction of initial propagation, after travelling some
distance.
In a progressive wave, the waveform is never reflected back.
Furthermore, if you are interested in applying the general
equation of speed for a wave (V = fλ) , you can apply it only
for a progressive wave. This is due to the fact that we are
considering the whole motion of the wave within a given time.
(In a stationary wave, this might not be so as within the time
interval specified, the wave might have reflected back!!)
Waves- By Aditya Abeysinghe

12. Principle of superposition
Principle:
The resultant displacement at any point is the sum of the separate
displacements due to the two waves.
Used for:
When two waves travel through a medium, their combined effect
at any point can be found by the principle of superposition.
Consider two waves in two occasions, where the amplitudes are
similar and dissimilar.
(i) When the amplitudes are similarWhen the amplitudes are similar but opposite in direction, the total
displacement of the wave at any point of similar phase is zero.
See the diagram:
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13. (ii) When the amplitudes are dissimilarWhen the amplitudes are dissimilar but opposite in direction, the total
displacement of the wave at any point of similar phase is not zero.
See the diagram:
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14. (iii) When the amplitudes are either similar or dissimilar, but the
two waves are travelling in the same direction:
The two waves travel
in the same direction
The two waves meet
at some point
This results in an increase of
amplitude. The amplitudes of
the two individual waves are
added up. This results in an
unstable equilibrium
Finally, stability occurs when
the two waves start travelling
in opposite ways.
Waves- By Aditya Abeysinghe
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15. Stationary or Standing waves
Consider the following apparatus:
Original
wave
Light string
Reflected
wave
Pulley
Vibrator vibrating at constant
frequency
Mass
When the mass is kept constant, the tension of the string is constant.
Furthermore, the pulley acts as a barrier for the further propagation of
the wave.
However, the vibrator continously produces vibrations on the string
surface. Therefore, at the pulley end, the wave returns or is reflected
along the initial direction of propagation.
Waves- By Aditya Abeysinghe
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16. This time the wave-like profile on the string
does not move along the medium, and the
wave is therefore called a stationary (or
standing) wave.
The stationary wave is due to the
superposition of two waves of equal
frequency and amplitude travelling in
opposite directions along the string.
The figure shows how the motion or the
behavior or the appearance of a stationary
wave changes with time.
Waves- By Aditya Abeysinghe
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17. t=0
t = T/8
t = T/4
t = 3T/8
t = T/2
Waves- By Aditya Abeysinghe
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18. Properties of stationary or
standing waves
Consider the stationary wave below:
Reflected
wave
Original
wave
The following points are important in understanding the behavior of a
standing wave:
1. There are points where the displacement is permanently zero.
These points are called the nodes of the stationary waves.
2. At points between successive nodes the vibrations are in phase.
Waves- By Aditya Abeysinghe
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19. 3. Each point along the wave has a different amplitude of
vibration from neighboring points. Points with the greatest
amplitude are called antinodes.
4. The wavelength, λ, of any type of stationary wave is twice
the distance between successive nodes or successive
antinodes. Thus, the distance between a node or an
antinode and the next node or the antinode is λ/2 and the
distance between a node and a neighboring antinode is λ/4.
Note:
The second and third points are in sharp contrast to the
behavior of a progressive wave, where the phase of points
near each other are all different and every point vibrates
with the same amplitude.
Waves- By Aditya Abeysinghe
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20. Stationary longitudinal waves
Stationary longitudinal waves can be studied when
considering the wave patterns inside a closed pipe.
In a closed pipe, the displacement of the particles near the
closed end should be zero and the displacement near the
open end should be maximum. So, the node of the wave
formed inside a closed pipe is on the closed end and the
antinode is near the open end.
Node
Antinode
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21. Stationary transverse waves
Stationary transverse waves behave in a similar
vein to that of stationary longitudinal waves.
Stationary transverse waves can be observed
when a string is tied at both ends and a vibration
is made on one of its ends.
Antinode
Node
Node
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22. Pressure in stationary wave
Consider the diagram below.
displacement
N
A
N
N
A
A
N
A
N
At the node, the particles on either side produce a compression
(increase of pressure), from the direction of their displacement. At the
same time, the particles near an antinode are zero. Thus, the pressure
is normal (decrease of pressure)
Normal pressure
pressure
N
A
N
A
N
Waves- By Aditya Abeysinghe
A
N
A
N
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