Fundamental Concepts of Waves and Motion

Waves and Types

Wave: A wave is a propagation of a disturbance of some property of a medium that propagates through space carrying energy.

• Longitudinal wave: A longitudinal wave is a wave in which the motion of the particles of the medium is parallel to the direction of propagation of the wave.
• Transverse wave: A transverse wave is a movement characterized by oscillations that occur perpendicular to the direction of propagation.
• Electromagnetic wave: An electromagnetic wave is the propagation of electromagnetic radiation through space.
• Mechanical wave: A mechanical wave is a disturbance (for example, a tension disturbance) that propagates through a material medium.

Wave Parameters

Length: The length is the distance between two points. The length of an object is the distance between its ends; it is its linear extension and a principal measure of size.

Period (T): The period is the time it takes for a repeated movement to complete one cycle.

Frequency (f): Frequency is the number of times the motion repeats in one second.

Formula: T = 1 / f (sometimes expressed as T = 1 / sampling in the context of sampled signals).

The speed of propagation: The speed of propagation is the ratio between the distance traveled by the mobile (object) and the travel time taken by the same: v = distance / time.

Reference Frames and Motion

Reference system: A reference system is a point or a set of points we use to determine whether a body moves.

Position: Position is measured relative to the origin of the reference system.

Displacement vector: Moving a mobile (for example, a mobile phone) defines a displacement vector that originates at the starting point of the movement and ends at the end point of the movement.

Speed / Velocity: The speed (or average velocity) of a body is the displacement per unit time: v = displacement (r) / time taken (t).

Acceleration: Acceleration measures the rate at which velocity varies with time. For a change from initial velocity Vi at time Ti to final velocity Vf at time Tf, A = (Vf - Vi) / (Tf - Ti). Acceleration is measured in m/s².

Kinematic Equations

• MRU (Uniform Rectilinear Motion): x_f = x₀ + v t
• MRUA (Uniformly Accelerated Motion): x_f = x₀ + v₀ t + (1/2) a t²
• Free fall: y_f = y₀ + v₀ t - (1/2) 9.8 t²

Rotational Motion

Angular velocity: Angular velocity is a measure of the speed of rotation. It is defined as the angle turned per unit time and is denoted by the Greek letter ω. Its SI unit is the radian per second (rad/s).

Angular acceleration: Angular acceleration is the change experienced by the angular velocity per unit time.

Centripetal acceleration: Centripetal acceleration is a quantity related to the change of direction (and thus the change of velocity vector) when a moving particle travels along a curved path.