Physics | Properties of waves

Welcome to the World of Waves!

Hello future physicists! This chapter, Properties of Waves, is fundamental to understanding how the world around us works. Whether it's the light that lets you read these notes, the sound of your favourite music, or the signals connecting your phone, it all relies on waves!

Don't worry if some concepts seem a little abstract—we will break them down using simple analogies and clear steps. By the end of these notes, you’ll be able to describe, calculate, and predict how waves behave! Let’s dive in!

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1. What Exactly Is a Wave?

The Core Idea

In physics, a wave is defined as a disturbance that transfers energy from one place to another without transferring matter.

• When a wave moves across the ocean, the water itself doesn't travel across the ocean; it just moves up and down. The energy is what moves forward!
• Waves require a medium (a substance) to travel through, but some, like light, can travel through a vacuum (empty space).

The Two Main Types of Waves

We classify waves based on how the particles in the medium vibrate compared to the direction the energy is travelling.

A) Transverse Waves

In a transverse wave, the direction of vibration of the particles is perpendicular (at a 90-degree angle) to the direction the wave is travelling.

• Analogy: Imagine shaking a rope up and down. The wave moves horizontally along the rope, but your hand and the rope particles only move vertically (up and down).
• Key Parts:
  • Crest: The highest point of the wave.
  • Trough: The lowest point of the wave.
• Examples: All electromagnetic waves (light, radio, microwaves), water ripples.

B) Longitudinal Waves

In a longitudinal wave, the direction of vibration of the particles is parallel (in the same direction) to the direction the wave is travelling.

• Analogy: Imagine pushing and pulling a Slinky toy. The coils compress and spread out, and the energy moves along the Slinky in the same direction as the push/pull.
• Key Parts:
  • Compression: Regions where the particles are crowded together (high pressure).
  • Rarefaction: Regions where the particles are spread apart (low pressure).
• Examples: Sound waves.

Memory Aid: TransVerse looks like the V in "vertical" or "vibrate perpendicular." LongItudinal looks like the L in "linear" or "vibrate parallel."

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2. Describing Waves: Key Terminology

To measure and compare waves, we need a set of standard terms. These terms are used for both transverse and longitudinal waves.

A) Amplitude (A)

The amplitude is the maximum displacement (or height) of a point on the wave from its undisturbed rest position (equilibrium line).

• What it means: Amplitude is directly related to the energy carried by the wave. A loud sound (more energy) has a greater amplitude than a quiet sound.
• Unit: Usually metres (m).

B) Wavelength (\(\lambda\))

The wavelength (symbol: lambda, \(\lambda\)) is the distance between one point on a wave and the identical point on the next wave.

• For transverse waves: Crest to crest, or trough to trough.
• For longitudinal waves: Centre of one compression to the centre of the next compression.
• Unit: Metres (m).

C) Frequency (f)

The frequency is the number of complete waves (or cycles) that pass a fixed point every second.

• Unit: Hertz (Hz). 1 Hz means 1 wave passes every second.

D) Period (T)

The period is the time taken for one complete wave to pass a fixed point.

• Period and frequency are opposites (inversely related): \[T = \frac{1}{f}\]
• Unit: Seconds (s).

Did you know? High frequency radio waves, like those used for Wi-Fi, oscillate billions of times per second (in the GHz range)!

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3. The Wave Equation: Calculating Speed

The speed of a wave depends on how quickly the waves are produced (frequency) and how long each wave is (wavelength).

The Formula

The relationship between wave speed (\(v\)), frequency (\(f\)), and wavelength (\(\lambda\)) is given by the wave equation:

\[v = f \lambda\]

Where:

• \(v\) = Wave Speed (m/s)
• \(f\) = Frequency (Hz)
• \(\lambda\) = Wavelength (m)

Don't worry if rearranging equations seems tricky. Here is the handy Wave Equation Triangle:

(Imagine a triangle with v on top, and f and \(\lambda\) on the bottom row.)

• To find speed (\(v\)), cover \(v\): \(v = f \times \lambda\)
• To find frequency (\(f\)), cover \(f\): \(f = v / \lambda\)
• To find wavelength (\(\lambda\)), cover \(\lambda\): \(\lambda = v / f\)

Step-by-Step Calculation Example

Question: A sound wave travels at 340 m/s and has a frequency of 500 Hz. What is its wavelength?

Step 1: Identify Known Variables
\(v = 340\) m/s
\(f = 500\) Hz
\(\lambda = ?\)

Step 2: Choose the Correct Formula
We need to find \(\lambda\): \(\lambda = v / f\)

Step 3: Substitute Values and Calculate
\(\lambda = 340 / 500\)
\(\lambda = 0.68\)

Step 4: State the Unit
The wavelength is 0.68 m.

Common Mistake Alert: Always ensure your units are consistent! If frequency is given in kHz, convert it to Hz before calculating (1 kHz = 1000 Hz).

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4. Wave Behaviour: Reflection, Refraction, and Diffraction

Waves don't just travel in straight lines; they interact with boundaries and obstacles in predictable ways.

A) Reflection

Reflection occurs when a wave hits a boundary between two different media and bounces back.

• Examples: Light hitting a mirror, sound creating an echo, water waves bouncing off a harbour wall.
• The Law of Reflection: The angle of incidence (angle of the incoming wave measured to the normal line) is always equal to the angle of reflection (angle of the reflected wave measured to the normal line).
• Crucially: Reflection does not change the speed, frequency, or wavelength of the wave.

B) Refraction

Refraction is the change in direction of a wave as it passes from one medium to another (e.g., from air to glass, or deep water to shallow water).

Why does it happen?

The change in medium causes the wave's speed to change. If the wave hits the boundary at an angle, one part of the wave slows down (or speeds up) before the other part, causing the entire wave to bend or change direction.

• Analogy: Imagine pushing a shopping trolley from smooth tarmac (fast medium) onto grass (slow medium) at an angle. The wheel that hits the grass first slows down, causing the trolley to steer towards the grass.
• When waves slow down (e.g., light entering glass), they bend towards the normal.
• When waves speed up (e.g., light leaving glass), they bend away from the normal.
• Note: The frequency of the wave remains unchanged during refraction.

C) Diffraction

Diffraction is the spreading out of waves when they pass through a gap (aperture) or travel around an obstacle.

Key Factor: Wavelength vs. Gap Size

The amount of diffraction depends on the size of the gap compared to the wavelength (\(\lambda\)) of the wave.

• Maximum Diffraction: Occurs when the size of the gap is approximately equal to the wavelength of the wave.
• Minimum Diffraction: Occurs when the gap is much wider than the wavelength. The waves pass through mostly undisturbed.

Example: Radio signals (which have long wavelengths) diffract easily around hills and buildings, allowing reception even if you don't have a direct line of sight to the transmitter. Light waves (very short wavelength) do not diffract noticeably around everyday objects, which is why you can't see around corners!

Well done! You have now covered the core properties and behaviors of waves. Review these concepts often, practice the wave equation, and remember those helpful analogies!