Understanding Wave Mechanics: A Deep Dive

Wave Motion

Wave motion refers to the transmission of a disturbance from one point to another without the net transport of matter.

Wave Classification

Based on Direction of Propagation

• One-dimensional waves: Propagate in a single direction.
• Two-dimensional waves: Propagate in two directions.
• Three-dimensional waves: Propagate in three directions.

Based on Medium of Propagation

• Mechanical waves: Require a material medium for propagation. Their speed depends on the characteristics of the medium.
• Electromagnetic waves: Do not require a material medium and can propagate in a vacuum (e.g., visible light).

Based on Direction of Disturbance

• Transverse waves: The direction of propagation is perpendicular to the direction of the disturbance.
• Longitudinal waves: The direction of propagation is parallel to the direction of the disturbance (e.g., compressing and releasing a spring).

Theorem of Mechanical Energy Conservation

If the work done (W) equals the change in kinetic energy (ΔEc), and the forces acting are conservative, then W = -ΔU, where U is the potential energy. Therefore, ΔEc = -ΔU.

Mechanical Energy

Mechanical energy (E) is the sum of kinetic and potential energy. The above expression indicates that when forces acting on a body are conservative, the mechanical energy remains constant.

Wave Attenuation

Waves weaken as they propagate away from the source, resulting in a decrease in intensity. For harmonic waves in a homogeneous and isotropic medium, the decrease in intensity corresponds to a decrease in wave amplitude. This decrease can be caused by attenuation or absorption.

Viscosity

Viscosity is the resistance of fluids to flow.

Huygens' Principle

Wave intensity decreases exponentially with distance traveled through the medium. Every point on a wavefront acts as a source of secondary wavelets, with the same speed and frequency as the initial wave. The envelope of these wavelets forms a new wavefront.

Principle of Superposition

When two or more waves propagate through the same medium, the resulting disturbance at each point is the sum of the disturbances each wave would produce individually.