Science (Double Award) | Waves

🌊 Comprehensive Study Notes: Waves 🌊

Welcome to the World of Waves!

Hello future physicists! This chapter, Waves, is central to understanding how energy moves around the universe—from the sound of your voice to the light that allows you to read these notes. Don't worry if this seems tricky at first; we will break down every concept, use easy analogies, and make sure you understand the fundamental ideas of how energy travels without transporting matter itself. Let’s dive in!

Section 1: The Basics of Wave Motion

1.1 Defining a Wave

In physics, a wave is defined as a mechanism that transfers energy from one point to another, without transferring the matter (the medium) itself.

Analogy: Imagine a stadium "Mexican Wave." The energy (the movement) travels around the stadium, but the people (the matter) stay in their seats!

1.2 Types of Media

Waves often travel through a medium (the substance they travel in, like air, water, or steel).

• Mechanical Waves: These require a medium to travel (e.g., sound waves, water waves).
• Electromagnetic (EM) Waves: These do not require a medium and can travel through a vacuum (empty space, like space between planets) (e.g., light, radio waves).

Section 2: Transverse and Longitudinal Waves

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

2.1 Transverse Waves

In a transverse wave, the direction of the oscillation (vibration of the particles) is perpendicular (at a 90° angle) to the direction of energy transfer.

• The wave shape consists of crests (highest points) and troughs (lowest points).
• Examples: All Electromagnetic (EM) waves (light, X-rays), ripples on water.

Memory Aid: Think of a rope tied to a wall. If you flick it up and down (perpendicular), the wave moves across the room.

2.2 Longitudinal Waves

In a longitudinal wave, the direction of the oscillation is parallel (in the same direction) to the direction of energy transfer.

• The wave consists of areas of high pressure called compressions (where particles are squashed together) and areas of low pressure called rarefactions (where particles are spread apart).
• Examples: Sound waves, primary seismic P-waves.

Memory Aid: Longitudinal sounds like "long lines." The movement is along the line of the energy flow.

Section 3: Measuring Wave Characteristics

To describe a wave, we use four key measurable properties:

3.1 Key Wave Quantities

• Amplitude (\(A\)): The maximum displacement (distance) of a point on the wave from its resting or equilibrium position.
  What it tells you: The larger the amplitude, the more energy the wave carries. (Units: meters, m)
• Wavelength (\(\lambda\)): The distance between a point on one wave and the identical point on the next wave (e.g., crest to crest, or compression to compression).
  (Units: meters, m)
• Frequency (\(f\)): The number of complete waves passing a point per second.
  (Units: Hertz, Hz, which is the same as waves per second, \(s^{-1}\))
• Period (\(T\)): The time taken for one complete wave to pass a fixed point.
  Relationship: Period is the inverse of frequency: \(T = 1/f\). (Units: seconds, s)

3.2 The Wave Equation

The speed at which a wave travels (wave speed, \(v\)) is linked directly to its frequency and wavelength.

Wave Speed = Frequency \(\times\) Wavelength

\[v = f \lambda\]

Where:

• \(v\) is the speed (in meters per second, m/s)
• \(f\) is the frequency (in Hertz, Hz)
• \(\lambda\) is the wavelength (in meters, m)

Section 4: Wave Interactions (Reflection, Refraction, Diffraction)

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

4.1 Reflection

Reflection is when a wave bounces off a boundary between two different media.

• The wave remains in the original medium.
• The Law of Reflection: The angle of incidence (\(i\)) equals the angle of reflection (\(r\)). These angles are measured relative to the normal (a line drawn perpendicular to the surface).
• Real-world Example: Seeing your face in a mirror (light reflection) or hearing an echo (sound reflection).

4.2 Refraction

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

Why does it happen? Refraction occurs because the wave changes speed as it enters the new medium.

• If the wave slows down (e.g., entering glass from air), it bends towards the normal.
• If the wave speeds up (e.g., entering air from glass), it bends away from the normal.

Analogy: Imagine a car driving off a smooth road (fast) onto mud (slow). The first tire to hit the mud slows down, causing the car to turn (refract).

4.3 Diffraction

Diffraction is the spreading out of waves as they pass through a gap or move around the edge of an obstacle.

• Diffraction is most noticeable (maximum spreading) when the size of the gap or obstacle is roughly equal to the wavelength (\(\lambda\)) of the wave.
• Did you know? This is why you can hear sounds around a corner even though you can't see the source—sound waves (large wavelength) diffract easily. Light waves (very small wavelength) do not diffract noticeably around large objects.

Section 5: Sound Waves

5.1 The Nature of Sound

Sound waves are longitudinal waves produced by vibrating objects. They are mechanical waves, meaning they require a medium (like air, water, or a solid) to travel. They cannot travel through a vacuum.

We perceive high frequency as high pitch, and large amplitude as high volume (loudness).

5.2 Speed of Sound

The speed of sound depends on the medium it travels through. Sound travels faster in denser, more rigid materials because the particles are closer together, allowing vibrations to be transmitted more quickly.

Speed order (fastest to slowest):
Solids (\(\approx 5000 \text{ m/s}\)) > Liquids (\(\approx 1500 \text{ m/s}\)) > Gases (\(\approx 330 \text{ m/s}\) in air at 0°C)

Section 6: The Electromagnetic Spectrum

The Electromagnetic (EM) Spectrum is a continuous spectrum of transverse waves. These waves travel through a vacuum at the constant speed of light.

Speed of all EM waves in a vacuum \(c = 3.0 \times 10^8 \text{ m/s}\)

6.1 Properties and Order of the Spectrum

All EM waves:

• Are transverse.
• Travel at the same speed in a vacuum (\(c\)).
• Transfer energy.
• Can be reflected, refracted, and diffracted.

The EM spectrum is ordered by increasing frequency and decreasing wavelength (and therefore increasing energy):

Radio \(\rightarrow\) Micro \(\rightarrow\) Infra-Red \(\rightarrow\) Visible \(\rightarrow\) Ultra-Violet \(\rightarrow\) X-ray \(\rightarrow\) Gamma

Memory Aid (Mnemonics): Raging Martians Invaded Venus Using X-ray Guns.

6.2 Uses and Hazards of EM Waves

The energy of EM waves increases significantly from Radio to Gamma rays. Higher energy waves are more ionizing and dangerous.

Type	Primary Uses	Hazards / Safety
Radio Waves (Low \(f\), Long \(\lambda\))	Broadcasting (TV, radio), communication.	Generally safe (low energy).
Microwaves	Satellite communication, heating food (microwave ovens).	Internal heating of body tissue. Shielding metal required in ovens.
Infra-Red (IR)	Heating, thermal imaging (night vision), remote controls.	Skin burns (from high intensity sources).
Visible Light	Sight, photography, optical fibers.	Eye damage (from very bright sources, e.g., lasers).
Ultra-Violet (UV)	Tanning beds, sterilisation, security marking, generating Vitamin D.	Skin cancer, premature aging, eye damage. Safety: Sunscreen, protective eyewear.
X-rays	Medical imaging (diagnostics), checking baggage security.	Cell mutation and damage (ionising radiation). Safety: Lead shielding, limited exposure time.
Gamma Rays (High \(f\), Short \(\lambda\))	Sterilising medical equipment, treating cancer (radiotherapy).	Severe cell mutation and death (highly ionising). Safety: Thick lead/concrete shielding, remote handling.

6.3 A Note on Visible Light

Visible light is the tiny portion of the EM spectrum we can see. It is split into colors (Red, Orange, Yellow, Green, Blue, Indigo, Violet - ROYGBIV).
Red has the lowest frequency (longest wavelength) and Violet has the highest frequency (shortest wavelength).

You’ve reached the end of the Waves chapter notes! By mastering the difference between transverse and longitudinal waves, understanding the wave equation, and knowing the order and uses of the EM spectrum, you are well-prepared for your exams. Keep practising those wave equation calculations!