Transverse Waves

In a transverse wave, the particles of the medium vibrate perpendicular (at right angles) to the direction in which the wave travels. The highest point of the wave is called the crest, and the lowest point is the trough.

Examples: Light waves, water waves on a surface, rope waves.

Longitudinal Waves

In a longitudinal wave, the particles of the medium vibrate parallel to the direction of wave travel. The wave consists of compressions (where particles are close together) and rarefactions (where particles are spread apart).

Example: Sound waves traveling through air.

Amplitude is the maximum displacement of a particle from its rest position. It relates to the energy of the wave—a bigger amplitude means more energy.

Wavelength (λ) is the distance between two consecutive points in a wave that are in the same phase, such as from crest to crest or compression to compression. It is measured in meters.

Frequency (f) is the number of complete wave cycles that pass a point per second. The SI unit is the Hertz (Hz), where 1 Hz = 1 cycle per second.

Period (T) is the time taken for one complete wave cycle. It is the reciprocal of frequency:

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

Wave Speed (v) is how fast the wave travels through the medium.

The relationship between wave speed, wavelength, and frequency is given by:

$v = f \times \lambda$

This is called the wave equation.

Worked Example

A water wave has a wavelength of 0.5 m and a frequency of 2 Hz. What is its speed?

Solution:

• Wavelength, λ = 0.5 m
• Frequency, f = 2 Hz
• Using v = fλ:
• v = 2 × 0.5 = 1 m/s

The wave travels at 1 meter per second.

Statement: An object will remain at rest or move with uniform velocity in a straight line unless acted upon by a net external force.

What is Inertia?

Inertia is the property of a body to resist any change in its state of motion or rest. It depends on mass—the greater the mass, the greater the inertia.

Types of Inertia:

• Inertia of rest: A book stays on a table until pushed.
• Inertia of motion: A passenger falls forward when a moving bus stops suddenly.
• Inertia of direction: Water spills from a bucket when it is suddenly swung and stopped.

Example in Tanzanian Context

When a daladala (minibus) suddenly brakes, passengers inside lurch forward. This happens because their bodies continue moving forward due to inertia of motion, even though the vehicle has stopped. This is why wearing a seat belt is important—it provides an external force to stop your body from continuing forward.

Statement: The rate of change of momentum of a body is directly proportional to the applied force and takes place in the direction of the force.

This leads to the famous equation:

$F = ma$

Where:

• F = force (measured in Newtons, N)
• m = mass (kg)
• a = acceleration (m/s²)

One Newton (1 N) is the force that gives a mass of 1 kg an acceleration of 1 m/s².

Worked Example

A motorcycle of mass 150 kg accelerates at 2 m/s². What force is needed?

Solution:

• m = 150 kg
• a = 2 m/s²
• F = ma = 150 × 2 = 300 N

A force of 300 N is required.

Linear momentum (p) is the product of mass and velocity:

$p = mv$

Momentum is a vector quantity (it has direction). The SI unit is kg·m/s.

Principle: When two or more bodies collide, the total linear momentum before the collision equals the total linear momentum after the collision, provided no external force acts on the system.

Mathematically for two objects: $m_1u_1 + m_2u_2 = m_1v_1 + m_2v_2$

Where:

• u = initial velocity
• v = final velocity

Types of Collisions

Elastic collision: Both momentum and kinetic energy are conserved. Objects bounce off each other.

Inelastic collision: Only momentum is conserved. Objects stick together after collision.

Worked Example

Two cricket balls collide. Ball A (mass 0.15 kg) moves at 5 m/s to the right, and Ball B (mass 0.15 kg) is stationary. After a perfectly elastic collision, Ball A comes to rest. What is Ball B's velocity?

Solution:

• Initial momentum = m₁u₁ + m₂u₂ = (0.15 × 5) + (0.15 × 0) = 0.75 kg·m/s
• After collision: Ball A is at rest, so momentum = m₂v₂ = 0.15 × v₂
• 0.75 = 0.15 × v₂
• v₂ = 5 m/s

Ball B moves at 5 m/s to the right.

In Tanzania, the principle of conservation of momentum is applied when analyzing road traffic accidents. Police and engineers study the momentum of vehicles before and after collisions to determine speeds and responsibilities. Additionally, understanding Newton's second law helps engineers design vehicle braking systems—the brakes must apply enough force to overcome the momentum of buses and trucks, which have much larger masses than passenger cars. This is why heavy vehicles like trucks on Tanzanian roads require longer stopping distances.