Physics (0625) | General properties of waves

General Properties of Waves (IGCSE Physics 0625)

Hello future physicists! This chapter is incredibly important because waves—from the light that lets you read this to the sound of your music—are how energy travels through the universe. Understanding the basic properties of waves gives you the foundation needed to master light, sound, and the entire electromagnetic spectrum. Let's dive into the fundamentals!

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1. What is a Wave? Energy Transfer without Matter Transfer (Core 3.1.1)

A wave is a disturbance that travels through a medium (or sometimes a vacuum), carrying energy from one point to another without permanently moving the matter itself.

Key Concept: Energy vs. Matter

When a wave moves, the energy moves forward, but the particles of the medium only oscillate (vibrate) around a fixed position.

• What transfers: Energy.
• What does NOT transfer: Matter (the medium).

Analogy: Imagine a crowd performing a 'Mexican wave' in a stadium. The wave moves around the stadium, but the people themselves only stand up and sit down—they don't travel to the next seat. The energy (the disturbance) is transferred, but the people (the matter) stay put.

We describe wave motion as being illustrated by vibrations in ropes and springs, and by experiments using water waves (like in a ripple tank). (Core 3.1.2)

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2. Anatomy of a Wave: Key Features (Core 3.1.3)

To describe a wave accurately, we need precise terms for its size, speed, and timing.

a) Measuring the Size of the Wave

• Crest (or Peak): The highest point of a transverse wave.
• Trough: The lowest point of a transverse wave.
• Amplitude (A): The maximum displacement of a particle from its rest (equilibrium) position.
• Amplitude relates directly to the energy carried by the wave. (Think of a loud sound wave having a large amplitude.)
• Unit: meters (m).
• Wavelength (\(\lambda\)): The distance between two consecutive identical points on a wave (e.g., crest to crest, or trough to trough).
• Unit: meters (m) or centimetres (cm).
• Wavefront: A line (or surface) connecting points on a wave that are all oscillating in step (in phase). They represent the transfer of energy.
• Example: The straight or circular lines seen on the surface of water in a ripple tank.

b) Measuring the Timing and Speed

• Frequency (f): The number of complete wavelengths (or oscillations) that pass a fixed point per unit time (usually per second).
• Unit: Hertz (Hz), where 1 Hz = 1 wave per second.
• Period (T): The time taken for one complete oscillation (one wave) to pass a fixed point.
• Frequency and Period are related: \(f = \frac{1}{T}\)
• Wave Speed (v): The distance moved by the wave energy per unit time.
• Unit: meters per second (m/s).

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3. The Fundamental Wave Equation (Core 3.1.4)

The speed of a wave, its frequency, and its wavelength are linked by a crucial mathematical relationship.

Wave Speed = Frequency × Wavelength

$$ v = f\lambda $$

Where:

• \(v\) is the speed (m/s)
• \(f\) is the frequency (Hz)
• \(\lambda\) is the wavelength (m)

Tip for calculations: Make sure all units are consistent (e.g., use m, m/s, and Hz). If you are given kHz or cm, you must convert them!

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4. Two Main Types of Waves

Waves are classified based on the direction in which the particles of the medium vibrate relative to the direction the energy travels (propagation).

a) Transverse Waves (Core 3.1.5)

In a transverse wave, the direction of vibration of the particles is at right angles (perpendicular) to the direction of propagation (energy transfer).

• Vibrations: Up and down (or side to side).
• Propagation: Forward.
• They form distinct crests (peaks) and troughs.

Examples of Transverse Waves:

• Electromagnetic radiation (light, radio waves, X-rays, etc.)
• Water waves (on the surface of the water)
• Seismic S-waves (secondary seismic waves)

b) Longitudinal Waves (Core 3.1.6)

In a longitudinal wave, the direction of vibration of the particles is parallel to the direction of propagation (energy transfer).

• Vibrations: Back and forth in the direction of travel.
• They do not have crests and troughs, but rather alternating regions of high and low pressure/density:
• Compression: A region where the particles are crowded together (high pressure/density).
• Rarefaction: A region where the particles are spread apart (low pressure/density). (Supplement 3.4.10)

Analogy: If you push a Slinky coil back and forth, you create compressions and rarefactions traveling along its length.

Examples of Longitudinal Waves:

• Sound waves
• Seismic P-waves (primary seismic waves)

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5. General Wave Phenomena

Waves exhibit three major behaviors when they interact with boundaries or obstacles: reflection, refraction, and diffraction. (Core 3.1.7)

a) Reflection

Reflection is the bouncing back of a wave when it meets a barrier or surface.

• The wave direction changes, but its speed, frequency, and wavelength remain the same.
• Example: An echo is the reflection of a sound wave.
• Reflection can be easily shown using a ripple tank by placing a flat barrier (plane surface) in the water. (Core 3.1.8a)

b) Refraction

Refraction is the change in direction (bending) of a wave when it changes its speed as it passes from one medium into another, or due to a change in the characteristics of the medium.

• When a wave slows down, it bends towards the normal.
• When a wave speeds up, it bends away from the normal.
• The frequency (f) remains constant, but the wave speed (v) and wavelength (\(\lambda\)) change, based on \(v = f\lambda\).

Ripple Tank Example (Core 3.1.8b):

• Refraction is shown when water waves move from deep water (where they are fast and have a long wavelength) into shallow water (where they are slow and have a short wavelength). The wave direction changes (bends) if the wavefront hits the boundary at an angle.

c) Diffraction

Diffraction is the spreading out of waves as they pass through a narrow opening (gap) or around the edge of an obstacle.

Example: You can hear sound (a longitudinal wave) from around a corner even if you cannot see the source (the light waves did not diffract enough).

Factors Affecting Diffraction (Core 3.1.7c, Supplement 3.1.9 & 3.1.10)

The amount of diffraction (the spreading) depends on two things:

1. Wavelength (\(\lambda\)): Greater diffraction occurs for waves with a longer wavelength.
2. Gap Size (G): Maximum diffraction occurs when the wavelength is approximately equal to the size of the gap (\(\lambda \approx G\)).

If the gap is much wider than the wavelength (\(G >> \lambda\)), the wave passes through almost straight, and little diffraction is observed.

Diffraction can be shown in a ripple tank by: (Core 3.1.8c, 3.1.8d)

• Passing waves through a narrow gap.
• Passing waves past a sharp edge.