Introduction

Before getting into the technicalities and specifics of diffraction and interference, why don't we have a quick recap or learn about the basics?

What are waves?

Definition of a wave

A wave is a propagation of a disturbance which transfers energy from one point in space to another without the physical transfer of matter. - the disturbance can be caused by vibration or an oscillation - the wave can also travel through a medium or a vacuum depending on its properties

Wave classification

Can be classified by nature [EM wave, mechanical wave], direction of oscillation [longitudinal, transverse] as well as mode of motion [progressive, stationary]

1. Nature of Wave

   1. Electromagnetic (EM) Waves:

      • These waves do not require a medium to propagate and can travel through a vacuum.
      • They consist of oscillating electric and magnetic fields that are perpendicular to each other and to the direction of wave propagation.
      • Examples include light waves, radio waves, X-rays, and gamma rays.

   2. Mechanical Waves:

      • These waves require a medium (solid, liquid, or gas) to travel through.
      • The wave propagates by causing the particles of the medium to oscillate.
      • Examples include sound waves, water waves, and seismic waves.

2. Direction of Oscillation

   1. Longitudinal Waves:

      • In longitudinal waves, the particles of the medium oscillate parallel to the direction of wave propagation.
      • These waves consist of compressions (regions of high pressure) and rarefactions (regions of low pressure).
      • A common example is a sound wave traveling through air.

   2. Transverse Waves:

      • In transverse waves, the particles of the medium oscillate perpendicular to the direction of wave propagation.
      • These waves can be visualized as peaks (crests) and valleys (troughs).
      • Electromagnetic waves and waves on a string are typical examples of transverse waves.

3. Mode of Motion

   1. Progressive Waves (Traveling Waves):

      • Progressive waves move continuously through the medium, transferring energy from one point to another.
      • These waves can be either longitudinal or transverse.
      • An example of a progressive wave is a wave moving along a string where the disturbance travels from one end to the other.

   2. Stationary Waves (Standing Waves):

      • Stationary waves are formed by the superposition of two waves of the same frequency and amplitude traveling in opposite directions.
      • Unlike progressive waves, stationary waves do not transfer energy from one point to another. Instead, they create fixed points called nodes (points of no displacement) and antinodes (points of maximum displacement).
      • Examples include the vibrations of a guitar string or the air columns in a pipe.

Wave terms

1. The phase is the state of the wave in its cycle while the phase difference represents the difference in cycle between two waves.
2. The wavelength is the distance travelled for it to complete one cycle.
3. The period is the time taken for the wave to travel one wavelength.
4. The crest and trough represent the points of maximum and minimum displacement of the wave. The particle is also momentarily at rest at these locations.
5. The rest or equilibrium position is the point of which the particle would be without any disturbances.

Key Formulae Summary:

1. Wave Speed
   The speed $v$ of a wave is given by the product of its frequency $f$ and wavelength $\lambda$:

$$ v = f \lambda $$

1. Frequency
   The frequency f of a wave is the number of oscillations per unit time:

$$ f = \frac{1}{T} $$

where T is the period of the wave (the time it takes for one complete oscillation).

1. Wavelength
   Wavelength $\lambda$ is the distance between two consecutive points in phase on the wave (e.g., crest to crest, trough to trough):

$$ \lambda = \frac{v}{f} $$

1. Standing Wave Condition
   For standing waves on a string fixed at both ends, the wavelengths $\lambda_n$ are given by:

$$ \lambda_n = \frac{2L}{n} $$

where:

• L is the length of the string,
• n is the mode number (integer).

The corresponding frequencies $f_n$ are:

$$ f_n = \frac{n v}{2L} $$