This document discusses different types of waves including electromagnetic waves, mechanical waves, and matter waves. Mechanical waves can be transverse waves where the medium moves perpendicular to the wave propagation or longitudinal waves where the medium moves parallel to propagation. Transverse waves include water waves and S-waves while longitudinal waves include sound waves. Progressive waves continuously travel in one direction while stationary waves are formed by the interference of two progressive waves traveling in opposite directions, resulting in some points that do not move at all. The document also provides an example mathematical problem to calculate wave parameters from a given wave equation.

1. Wave and Oscillations

2. Objectives
Wave and Oscillations

3. Wave
o A wave is a propagating dynamic disturbance (change from equilibrium) of one or more quantities.. It may take the
form of elastic deformation, a variation of pressure, electric or magnetic intensity, electric potential, or temperature.
✔ Introduction of Waves
• Transfers energy.
• Usually involves a periodic, repetitive Movement.
• Does not result in a net movement of the medium or particles in the
medium (mechanical wave).

4. Waves-types
1. Electromagnetic Waves:
Electromagnetic waves are created by a fusion of electric
and magnetic fields. The light you see, and the colors
around you are visible because of electromagnetic waves.
e.g. Radio signals, light rays, x-rays, and cosmic rays
2. Mechanical waves:
A wave which needs a medium in order to propagate
itself. Sound waves, waves in a Slinky, and water waves
are all examples of this..
Based on the orientation of particle motion and
direction of energy, there are three categories:
1. Electromagnetic Wave
2. Mechanical Wave
3. Matter Wave
a. Transverse Wave
b. Longitudinal
Wave

5. Waves-types
a. Transverse Waves
Waves in which the medium moves at right angles to the direction of the wave.
There are two types of Mechanical waves are given below.
Examples of transverse waves:
Water waves (ripples of gravity waves, not sound through water), Light waves, S-wave earthquake waves, tringed
instruments, Torsion wave
The high point of a transverse wave is a crest. The low part is a trough.

6. Waves-types
b. Longitudinal Wave:
A longitudinal wave has the movement of the particles in the medium in the same dimension as the direction of
movement of the wave.
Examples of longitudinal waves:
Sound waves, P-type earthquake waves, Compression wave

7. Waves-types
In 1924, Luis de Broglie (Nobel Prize in Physics in 1929) proposed that a wave function is associated with all
particles. Where this wave function has nonzero amplitude, we are likely to find the particle. The standard
interpretation is that the intensity of the wave function of a particle at any point is proportional to the probability of
finding the particle at that point. The wave function for a material particle is often called a matter wave.
Matter Waves are associated with moving particles and are the result of the motion of electrons, protons, neutrons,
and other fundamental particles along with atoms and molecules. As its major constituent is matter hence these are
known as matter waves.
Matter Wave:
Photons are particles of light. Matter is made of atoms, and atoms are made of protons, neutrons, and
electrons. These are not macroscopic particles. Typical atomic dimensions are on the order of 10-10 m,
nuclear dimensions are on the order of 10-15 m, and the electron seems to be a point particle with no size at
all. How do these particles behave?
If a wave equation describes the behavior of photons, maybe a wave equation also
describes the behavior of other microscopic particles.

8. Waves-types

9. Progressive Wave and Stationary Wave
Progressive Wave
A wave which travels continuously in a medium in the same direction without a change in its amplitude is
called a travelling wave or a progressive wave or Travelling wave. Light wave is a progressive wave.
Stationary Wave
A stationary (or standing) wave is a wave formed by the superposition of two progressive waves of the same
frequency and amplitude traveling in the opposite direction
Wave Equation:
y(x,t) = A sin(kx - ωt) + A sin(kx + ωt)
y(x,t) = 2A sin(kx)cos(ωt)

10. Progressive and stationary waves-difference
Progressive waves Stationary waves
The disturbance produced in the medium travels
onward, it being handed over from one particle to
the next. Each particle executes the same type of
vibration as the preceding one, though not at the
same time.
There is no onward motion of the disturbance as no
particle transfers its motion to the next. Each
particle has its own characteristic vibration.
The amplitude of each partide is the same but the
phase changes continuously,
The amplitudes of the different particles are
different, ranging from zero at the nodes to
maximum at the antinodes. All the particles in each
segment vibrate in phase but in opposite phase
relative to the particles in the adjacent segment.
No particle is permanently at rest. Different
particles attain the state of momentary rest at
different instants,
The particles at the nodes are permanently at rest
but other particles attain their position of
momentary rest simultaneously.
All the particles attain the same maximum velocity
when they pass through their mean positions.
All the particles attain their own maximum velocity
at the same time when they pass through their mean
positions.
There is a flow of energy across every plane in the
direction of propagation.
Energy is not transported across any plane

11. Mathematical problems
Q1. A wave displacement is given by y = 0.1 sin (0.1x – 0.1t) m. Find (a) the amplitude of the wave, (b) the magnitude of
the propagation vector, (c) the wavelength, (d) the time period, and (e) the wave velocity
The various parameters of the given harmonic wave can be found by comparing it with the standard form
y = A sin (kx – ωt) for a wave propagating in the positive x-direction.
Solution:
(a) The amplitude A = 0.1 m
(b) The propagation vector k = 0.1 m–1
(c) The wavelength λ = 2π/k = 20π m
(d) The angular frequency ω = 0.1 s–1, time period T = 2π/ω = 20π s
(e) The wave velocity v = ω/k = 1 m/s.
y = 0.1 sin (0.1x – 0.1t)

12. Conclusions
Thank
you