Wave Properties and Behavior Study Notes

Introduction to Wave Properties

• Waves are a means of transferring energy without transferring matter.

• They can be categorized into two main types: transverse waves and longitudinal waves.

Wave Characteristics

• A wave can be described using the following characteristics:

  • Speed (v): The rate at which a wave travels through a medium, measured in $m/s$.

  • Amplitude (A): The height of a wave measured from its undisturbed position, indicating the energy of the wave, also measured in $m$.

  • Frequency (f): The number of oscillations (or vibrations) per second, measured in hertz (Hz).

  • Wavelength (λ): The distance between two successive crests or troughs of a wave, measured in metres (m).

• Relationship between speed, frequency, and wavelength can be defined by the wave equation:

  • $v = f \lambda$

    • Where $v$ = wave speed, $f$ = frequency, $\lambda$ = wavelength.

Types of Waves

• Transverse Waves:

  • The medium moves at right angles to the direction of wave travel.

  • Examples include ripples on water, light waves, and seismic S waves.

• Longitudinal Waves:

  • The medium moves in the same direction as the wave.

  • Examples include sound waves, seismic P waves.

  • Compressions and rarefactions characterize longitudinal waves:

    • Compression: Region where particles are close together.

    • Rarefaction: Region where particles are spread apart.

Wave Speed

• Different types of waves travel at different speeds:

  • Light waves approximate $3 \times 10^8 m/s$.

  • Sound waves travel around $330 m/s$ in air and vary based on medium.

Wave Behavior

Reflection

• Reflection occurs when a wave hits a barrier, changing its direction according to the law of reflection:

  • Law of Reflection: $\text{Angle of incidence} = \text{Angle of reflection}$

Refraction

• Refraction is the bending of waves when they pass from one medium to another, causing a change in speed:

  • Light bends toward the normal when entering a denser medium (e.g., air to glass).

  • Light bends away from the normal when exiting a denser medium (glass to air).

Diffraction

• Diffraction is the spreading out of waves when they pass through a gap or around an obstacle:

  • Greater diffraction occurs if the gap size is close to the wavelength of the wave.

Behavior of Light Waves in Lenses and Mirrors

Ray Diagrams for Reflection

• Ray diagrams illustrate the pathway of light rays, helping us determine the characteristics of images formed by mirrors:

  • The normal line is drawn perpendicular to the mirror at the point where the ray hits.

  • The angles of incidence and reflection are measured from this normal.

Image Formation in a Plane Mirror

• Images in a plane mirror are:

  • Virtual (cannot be projected on a screen).

  • Laterally inverted (left and right are switched).

  • The same size as the object and located the same distance behind the mirror as the object is in front.

Lenses

• A converging lens focuses parallel rays to a single point called the principal focus:

  • The focal length is the distance from the lens to the focal point.

• A magnifying glass is a converging lens used to produce a virtual, magnified image.