Welcome to the World of Waves!
Have you ever watched ripples spread across a pond, listened to your favourite song through headphones, or had an X-ray taken? All of these involve waves! In this chapter, we are going to explore how waves work, how they transfer energy, and how we use them in everyday life.
Don't worry if physics sometimes feels intimidating! We will break down every single idea into simple, bite-sized steps with clear examples and memory tricks so you can master this topic for your GCSE exam.
1. What Exactly is a Wave?
A wave is a disturbance that transfers energy and information from one place to another without transferring matter.
The Stadium Analogy: Imagine doing "the wave" in a sports stadium. When it reaches you, you stand up and sit back down. You do not run around the stadium; only the pattern (the energy) travels around the crowd. The people (matter) stay in their seats!
Did you know? When you speak to a friend across the room, the air particles do not travel from your mouth to their ear. The air particles simply vibrate back and forth, passing the sound energy along.
Key Takeaway: Waves carry energy, not matter.
2. The Two Main Types of Waves
Waves are classified based on the direction in which the particles vibrate (oscillate) compared to the direction the energy travels.
A. Transverse Waves
In a transverse wave, the vibrations are perpendicular (at a right angle, \(90^\circ\)) to the direction of energy transfer.
• Motion: Particles move up and down while the wave travels left to right.
• Key features: The highest point is called a crest (or peak) and the lowest point is called a trough.
• Examples: Light waves, all other electromagnetic waves (like radio and microwaves), water surface waves, and S-waves in earthquakes.
B. Longitudinal Waves
In a longitudinal wave, the vibrations are parallel (in the same direction) to the direction of energy transfer.
• Motion: Particles vibrate back and forth along the line of wave travel.
• Key features:
- Compression: A region where particles are pushed close together (high pressure).
- Rarefaction: A region where particles are spread far apart (low pressure).
• Examples: Sound waves, ultrasound, and P-waves in earthquakes.
Memory Trick:
• Transverse = T-shaped (perpendicular, like the letter \(T\)).
• Longitudinal = Line (vibrations along the same line as the wave).
Key Takeaway: Transverse waves vibrate at \(90^\circ\) to energy travel; longitudinal waves vibrate parallel to energy travel.
3. Describing Waves: Key Terms & Definitions
To talk about waves like a physicist, you need to know these four essential terms:
• Amplitude (\(A\)): The maximum displacement of a particle from its rest position (undisturbed position). Measured in metres (\(\text{m}\)). On a wave diagram, this is the height from the centre line to a crest, or from the centre line to a trough.
• Wavelength (\(\lambda\)): The distance between two identical points on consecutive waves, such as from one crest to the next crest, or from one compression to the next compression. Measured in metres (\(\text{m}\)). We use the Greek letter lambda (\(\lambda\)) for this.
• Frequency (\(f\)): The number of complete waves passing a point every second. Measured in Hertz (\(\text{Hz}\)). For example, a frequency of \(50\text{ Hz}\) means \(50\) complete waves pass every single second.
• Period (\(T\)): The time taken for one complete wave to pass a point. Measured in seconds (\(\text{s}\)).
The Relationship Between Frequency and Period
Period and frequency are inversely related by the formula:
\(T = \frac{1}{f}\) or \(f = \frac{1}{T}\)
Common Mistake to Avoid: Amplitude is measured from the middle line to the peak, NOT from the very bottom (trough) to the top (crest)!
Key Takeaway: Wavelength is the length of one full cycle; frequency is how many cycles happen per second; amplitude shows the wave's maximum height from the middle.
4. The Wave Equations
In your exam, you will need to calculate wave speed using two main equations.
Equation 1: The Wave Equation
\(v = f \times \lambda\)
Where:
• \(v\) = wave speed in metres per second (\(\text{m/s}\))
• \(f\) = frequency in Hertz (\(\text{Hz}\))
• \(\lambda\) = wavelength in metres (\(\text{m}\))
Worked Example:
A sound wave has a frequency of \(440\text{ Hz}\) and a wavelength of \(0.75\text{ m}\). Calculate the speed of the wave.
Step 1: Write down the formula: \(v = f \times \lambda\)
Step 2: Substitute the values: \(v = 440 \times 0.75\)
Step 3: Calculate: \(v = 330\text{ m/s}\)
Equation 2: Speed, Distance, and Time
Since waves travel at a certain speed, you can also use the standard speed equation:
\(v = \frac{d}{t}\)
Where:
• \(v\) = speed in metres per second (\(\text{m/s}\))
• \(d\) = distance in metres (\(\text{m}\))
• \(t\) = time in seconds (\(\text{s}\))
Key Takeaway: Wave speed can be found by multiplying frequency by wavelength (\(v = f\lambda\)) or by dividing distance by time (\(v = \frac{d}{t}\)).
5. Measuring the Speed of Sound & Echo Calculations
Measuring Sound Speed in the Lab
To measure the speed of sound in air:
1. Stand a known large distance (\(d\)) away from a flat wall or another person (e.g., \(100\text{ m}\)).
2. Make a sharp, loud noise (e.g., clapping two wooden blocks together).
3. Use a stopwatch to record the time (\(t\)) taken to hear the echo, or the time between seeing the blocks hit and hearing the sound.
4. Calculate speed using \(v = \frac{d}{t}\).
Echo Calculations (Sonar and Radar)
An echo is a reflected sound wave. Because the sound must travel to the barrier and then bounce back, the sound travels double the distance (\(2d\)).
\(v = \frac{2d}{t}\) or \(d = \frac{v \times t}{2}\)
Worked Example:
A ship uses sonar to find the depth of the seabed. It sends a pulse of ultrasound into the water. The echo returns \(0.8\text{ s}\) later. The speed of sound in water is \(1500\text{ m/s}\). Calculate the depth of the water.
Step 1: Find total distance travelled: \(d_{\text{total}} = v \times t = 1500 \times 0.8 = 1200\text{ m}\)
Step 2: Divide by \(2\) because the pulse travelled down and back: \(\text{Depth} = \frac{1200}{2} = 600\text{ m}\)
Common Mistake to Avoid: Always check if an echo is involved! If so, remember to divide the total distance by \(2\) to find the depth or one-way distance.
Key Takeaway: Echoes involve a two-way journey, so always account for the double distance (\(2d\)).
6. Wave Behaviour: Reflection and Refraction
A. Reflection
When a wave hits a smooth barrier and bounces off, this is called reflection.
• The line drawn perpendicular (\(90^\circ\)) to the surface is the normal.
• The angle of incidence (\(i\)) is the angle between the incoming (incident) ray and the normal.
• The angle of reflection (\(r\)) is the angle between the reflected ray and the normal.
• The Law of Reflection: \(\text{Angle of incidence } (i) = \text{Angle of reflection } (r)\)
B. Refraction
Refraction is the change in direction of a wave as it passes from one medium into another, caused by a change in speed.
• When a wave enters a denser material (e.g., light going from air into glass), it slows down and bends towards the normal.
• When a wave enters a less dense material (e.g., light going from glass into air), it speeds up and bends away from the normal.
• Important note: During refraction, the frequency stays constant, but the wavelength changes along with the speed!
Key Takeaway: Reflection involves bouncing at equal angles (\(i = r\)); refraction involves changing speed and bending when crossing into a new material.
7. Ultrasound
Humans can hear sound frequencies between roughly \(20\text{ Hz}\) and \(20\text{, }000\text{ Hz}\) (\(20\text{ kHz}\)).
Ultrasound is defined as sound waves with a frequency greater than \(20\text{, }000\text{ Hz}\) (above the upper limit of human hearing).
Uses of Ultrasound:
• Prenatal Scanning (Foetal Scans): Ultrasound pulses are sent into the body. They partially reflect at boundaries between different tissues (e.g., between fluid and bone). A computer calculates the time delays to build up an image of the unborn baby. It is completely safe because ultrasound is non-ionising (unlike X-rays).
• Sonar / Depth Sounding: Ships use ultrasound to detect fish or measure water depth.
• Cleaning Delicate Objects: High-frequency vibrations in a liquid bath shake dirt off jewellery or surgical instruments.
Key Takeaway: Ultrasound has a frequency above \(20\text{, }000\text{ Hz}\) and is widely used for non-invasive medical imaging and sonar.
8. The Electromagnetic (EM) Spectrum
The electromagnetic spectrum is a continuous family of transverse waves that all share key properties:
1. They are all transverse waves.
2. They all travel at the same speed in a vacuum: the speed of light, which is \(3 \times 10^8\text{ m/s}\) (\(300\text{, }000\text{, }000\text{ m/s}\)).
3. They can all travel through a vacuum (empty space) without needing particles.
The Order of the Spectrum
From longest wavelength / lowest frequency to shortest wavelength / highest frequency:
1. Radio Waves (Longest wavelength, lowest frequency, lowest energy)
2. Microwaves
3. Infrared (IR)
4. Visible Light (Red, Orange, Yellow, Green, Blue, Indigo, Violet)
5. Ultraviolet (UV)
6. X-rays
7. Gamma Rays (Shortest wavelength, highest frequency, highest energy)
Memory Mnemonic:
Raging Martians Invaded Venus Using X-ray Guns
(Radio, Microwave, Infrared, Visible, Ultraviolet, X-ray, Gamma)
Uses and Dangers of EM Waves
• Radio Waves: Used for television and radio broadcasting. No known significant danger at normal levels.
• Microwaves: Used for satellite communications, mobile phones, and cooking food. Danger: Can cause internal heating of body tissues.
• Infrared: Used for TV remote controls, thermal imaging cameras, and radiant heaters. Danger: Can cause skin burns.
• Visible Light: Used for human vision, photography, and fibre optic communications.
• Ultraviolet: Used for sunbeds, detecting forged bank notes, and sterilisation. Danger: Can damage skin cells leading to sunburn, premature ageing, and skin cancer, and can cause cataracts in eyes.
• X-rays: Used for medical imaging of bones and airport luggage security. Danger: Ionising radiation can cause gene mutations and increase cancer risk.
• Gamma Rays: Used for sterilising medical instruments and treating cancer (radiotherapy). Danger: High-energy ionising radiation can cause severe cell damage and cancer.
Key Takeaway: As you move from Radio to Gamma, frequency and energy increase, while wavelength decreases. Higher frequency waves (UV, X-ray, Gamma) are ionising and hazardous.
Quick Review Summary
• Waves transfer energy without transferring matter.
• Transverse waves have oscillations at \(90^\circ\) to wave direction; Longitudinal waves oscillate parallel to wave direction.
• Use \(v = f\lambda\) and \(v = \frac{d}{t}\) for wave calculations.
• For echoes, remember the signal travels there and back: \(\text{distance} = 2d\).
• Ultrasound (\(> 20\text{, }000\text{ Hz}\)) is safe for medical imaging because it is non-ionising.
• All EM waves travel at \(3 \times 10^8\text{ m/s}\) in a vacuum; frequency increases from Radio to Gamma.