Science (Single Award) | Waves

🌊 Comprehensive Study Notes: Waves 🌊

Introduction: Why Do We Study Waves?

Hello future Physicists! Welcome to the exciting world of Waves. Don't worry if this topic seems tricky at first; we’re going to break it down using simple steps and everyday examples.

Waves are everywhere! They bring you sunlight, allow you to hear music, and carry signals to your phone. Simply put, a wave is a way of transferring energy from one place to another without permanently moving the matter itself. Understanding waves is essential because they are the basis of communication and energy transfer across the universe. Let’s dive in!

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1. The Basics: Energy Transfer vs. Matter Transfer

The most crucial idea in this chapter is:

• Waves transfer energy.
• Waves do NOT transfer matter.

Analogy: The Stadium Mexican Wave
When people do the "Mexican Wave" in a stadium, the energy (the wave) travels around the stadium, but the people (the matter/medium) just stand up and sit down in the same place. They don't move across the stadium. Waves behave the same way!

Key Term: Medium

The medium is the material (like air, water, or a string) through which a wave travels. Some waves, like light, don’t need a medium and can travel through a vacuum (empty space).

2. Types of Waves: Transverse and Longitudinal

We categorize waves based on how the particles in the medium vibrate compared to the direction the energy travels.

2.1. Transverse Waves

In a transverse wave, the vibration (oscillation) of the medium is at right angles (perpendicular) to the direction the wave is travelling.
Think: Up and down movement, but the wave goes forward.

• Examples: All electromagnetic waves (light, radio), ripples on water, waves on a string.
• Key Features: They have Crests (the highest points) and Troughs (the lowest points).

2.2. Longitudinal Waves

In a longitudinal wave, the vibration of the medium is parallel to the direction the wave is travelling.
Think: Back and forth movement, and the wave goes forward.

• Examples: Sound waves, seismic P-waves (primary waves).
• Key Features: They consist of Compressions (where particles are squashed together) and Rarefactions (where particles are spread apart).

🔥 Memory Aid 🔥
Transverse: Think of a "T" shape – perpendicular.
Longitudinal: Think of lines that are Lined up – parallel.

3. Describing Waves: Key Terminology

To measure and compare waves, we use specific terms:

1. Wavelength (\(\lambda\), lambda):
   This is the distance from one point on a wave to the exact same point on the next wave (e.g., crest to crest, or compression to the next compression).
   Unit: Metres (m).
2. Amplitude (A):
   This is the maximum displacement (distance) of a point on the wave from its resting position (equilibrium). The bigger the amplitude, the more energy the wave is carrying.
   For sound, higher amplitude means louder sound. For light, higher amplitude means brighter light.
   Unit: Metres (m).
3. Frequency (f):
   This is the number of complete waves passing a point every second.
   Unit: Hertz (Hz). (1 Hz = 1 wave per second).
4. Period (T):
   This is the time it takes for one complete wave to pass a fixed point.
   Unit: Seconds (s).

Did you know? Frequency and Period are inverses of each other! \[T = \frac{1}{f} \quad \text{and} \quad f = \frac{1}{T}\]

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4. The Wave Equation: Calculating Speed

The speed at which a wave travels depends on its frequency and wavelength. This relationship is always true for any wave!

The Wave Speed Formula

Wave Speed = Frequency × Wavelength \[v = f \times \lambda\]

Where:
\(v\) = Wave speed (m/s)
\(f\) = Frequency (Hz)
\(\lambda\) = Wavelength (m)

Step-by-Step Calculation Example

Example: A wave has a frequency of 50 Hz and a wavelength of 0.5 m. What is its speed?

1. Identify Knowns: \(f = 50 \text{ Hz}\), \(\lambda = 0.5 \text{ m}\).
2. State Formula: \(v = f \times \lambda\).
3. Substitute and Solve: \(v = 50 \text{ Hz} \times 0.5 \text{ m} = 25 \text{ m/s}\).
4. State Units: The wave speed is 25 metres per second.

🚨 Common Mistake Alert! 🚨
Always check your units! If the wavelength is given in cm, you MUST convert it to metres (m) before using the formula. (Divide cm by 100).

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5. Behaviour of Waves: Reflection and Refraction

When waves meet a boundary between two different materials (or media), they can change direction.

5.1. Reflection (The Bounce)

Reflection happens when a wave hits a surface or boundary and bounces back.
Think: Light hitting a mirror, or sound echoing off a wall.

• The key rule is the Law of Reflection: The angle of incidence (the angle the incoming wave hits the surface at) is equal to the angle of reflection (the angle the outgoing wave leaves at).
• Reflection does NOT change the wave speed, frequency, or wavelength.

5.2. Refraction (The Bend)

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

Why does it bend?

• When a wave changes medium (e.g., light going from air into glass), its speed changes.
• This change in speed causes the wave to change direction (to bend), unless it hits the boundary at 90°.

Analogy: A car drives from a smooth road (fast medium) onto muddy ground (slow medium) at an angle. The tyre that hits the mud first slows down, causing the car to turn/bend towards the slower medium.

Key Takeaway: Reflection is bouncing off; Refraction is bending caused by a change in wave speed.

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6. The Electromagnetic (EM) Spectrum

The Electromagnetic Spectrum is the family of waves that are all transverse waves and travel at the same speed in a vacuum (the speed of light, approximately \(3 \times 10^8 \text{ m/s}\)).
The waves are grouped by their wavelength and frequency.

As you move along the spectrum from Radio waves to Gamma rays:

• Wavelength (\(\lambda\)) Decreases
• Frequency (\(f\)) Increases
• Energy Increases (Gamma rays carry the most energy)

The Order of the EM Spectrum

It is crucial to know the order of the EM spectrum (from longest wavelength/lowest frequency to shortest wavelength/highest frequency):

Radio waves
Microwaves
Infrared (IR)
Visible light
Ultraviolet (UV)
X-rays
Gamma rays

💡 Mnemonic:
Really Many Invisible Visitors Use Xtra Gadgets

Uses and Dangers of EM Waves

Wave Type	Typical Use	Potential Danger/Risk
Radio	Communication (TV, broadcasting)	Generally harmless
Microwaves	Heating food, satellite communication	Internal heating of body tissue
Infrared (IR)	Heating (toasters), remote controls, thermal cameras	Skin burns (overheating)
Visible Light	Seeing, photography, optical fibres	Damage to retina if too intense
Ultraviolet (UV)	Tanning beds, sterilisation, security marking	Skin cancer, eye damage, premature ageing
X-rays	Medical imaging (broken bones), airport security	Ionising radiation, cell mutation
Gamma Rays	Sterilising medical equipment, treating cancer (radiotherapy)	Highly ionising, severe cell damage

Important Note for Single Award: The higher the frequency (closer to Gamma rays), the more energy the wave carries, and the more dangerous it is because it is ionising (it can knock electrons out of atoms, damaging DNA).

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Chapter Summary: Key Takeaways

You are now a wave expert! Remember these core concepts:

• Waves transfer energy, not matter.
• Transverse waves vibrate perpendicular to travel (Light).
• Longitudinal waves vibrate parallel to travel (Sound).
• Wave speed is calculated using the equation: \(v = f \times \lambda\).
• Refraction is bending due to a change in speed.
• The EM spectrum ranges from low-energy Radio waves (long wavelength) to high-energy Gamma rays (short wavelength).

Keep practicing the wave equation and the EM spectrum order, and you'll ace this chapter! Great work!