Welcome to Topic 2.1: Waves
Welcome to your study notes for Waves, a core topic in Unit 2 of your CCEA GCSE Physics course. Waves are all around us every day—from the light that allows us to see, to the sound of music, to the Wi-Fi signals connecting our phones. Don't worry if physics sometimes feels challenging; we will break down each idea step-by-step with clear definitions, helpful analogies, and exam tips so you can tackle any question with confidence!
1. The Fundamental Nature of Waves
What exactly is a wave? In physics, a wave is a disturbance that transfers energy from one place to another without transferring matter.
Analogy: Imagine doing "the wave" in a sports stadium. When you stand up and sit down, you stay in your seat, but the wave travels all the way around the stadium. Energy moves, but the people (the matter) stay where they are!
Two Main Types of Waves
Waves are sorted into two main categories depending on how the particles vibrate compared to the direction the energy travels:
1. Transverse Waves
In a transverse wave, the oscillations (vibrations) of the particles are perpendicular (at right angles, \(90^\circ\)) to the direction of wave travel (energy propagation).
• Examples: All electromagnetic waves (such as light and radio waves), water surface ripples, and seismic S-waves.
2. Longitudinal Waves
In a longitudinal wave, the oscillations (vibrations) of the particles are parallel to the direction of wave travel (energy propagation).
As a longitudinal wave moves, it squashes and stretches the medium, creating two distinct regions:
• Compressions: Regions of high particle density and high pressure where particles are pushed close together.
• Rarefactions: Regions of low particle density and low pressure where particles are spread apart.
• Examples: Sound waves, ultrasound, and seismic P-waves.
Quick Review & Memory Tip:
• Transverse = T-shaped (perpendicular / right angles).
• Longitudinal = Line (parallel vibrations along the same line as energy travel).
Key Takeaway: Waves transfer energy, not matter. Transverse waves vibrate perpendicular to the direction of travel; longitudinal waves vibrate parallel to the direction of travel and have compressions and rarefactions.
2. Wave Properties & The Wave Equation
To describe waves accurately, we use four essential measurements:
1. Amplitude (\(A\))
The amplitude is the maximum displacement of a point on a wave from its undisturbed (rest or equilibrium) position. Measured in metres (\(\text{m}\)).
Common Mistake Alert: Always measure amplitude from the central rest line to the top of a crest (peak) or to the bottom of a trough. Do not measure from peak to trough!
2. Wavelength (\(\lambda\))
The wavelength (symbolised by the Greek letter lambda, \(\lambda\)) is the distance between two consecutive identical points on a wave. Measured in metres (\(\text{m}\)).
• On a transverse wave: from one crest to the next crest, or one trough to the next trough.
• On a longitudinal wave: from the centre of one compression to the centre of the next compression.
3. Frequency (\(f\))
The frequency is the number of complete waves produced per second, or the number of waves passing a fixed point each second. Measured in Hertz (\(\text{Hz}\)), where \(1\text{ Hz} = 1\text{ wave per second}\).
4. Periodic Time (\(T\))
The periodic time (or period) is the time taken in seconds for one complete wave cycle to pass a fixed point.
Frequency and periodic time are linked by the formulae:
\(T = \frac{1}{f}\) or \(f = \frac{1}{T}\)
The Wave Speed Equation
All waves obey the fundamental wave equation linking speed, frequency, and wavelength:
\(v = f \lambda\)
Where:
• \(v =\) wave speed in metres per second (\(\text{m/s}\))
• \(f =\) frequency in hertz (\(\text{Hz}\))
• \(\lambda =\) wavelength in metres (\(\text{m}\))
Formula Triangle Trick: Put \(v\) at the top, with \(f\) and \(\lambda\) at the bottom.
• To find speed: \(v = f \times \lambda\)
• To find frequency: \(f = \frac{v}{\lambda}\)
• To find wavelength: \(\lambda = \frac{v}{f}\)
Unit Conversion Reminder:
Examiners often give values in units you must convert before calculating:
• Kilohertz to Hertz: \(1\text{ kHz} = 10^3\text{ Hz} = 1\,000\text{ Hz}\)
• Megahertz to Hertz: \(1\text{ MHz} = 10^6\text{ Hz} = 1\,000\,000\text{ Hz}\)
• Centimetres to Metres: \(1\text{ cm} = 0.01\text{ m}\) (divide by \(100\))
• Millimetres to Metres: \(1\text{ mm} = 0.001\text{ m}\) (divide by \(1\,000\))
Key Takeaway: Amplitude is rest-to-peak distance, wavelength is peak-to-peak distance, and frequency is waves per second. Use \(v = f \lambda\) with standard units (\(\text{m/s}\), \(\text{Hz}\), \(\text{m}\)).
3. Sound and Ultrasound
The Nature of Sound
Sound is a longitudinal mechanical wave caused by vibrating particles. Because it requires particles to pass on vibrations, sound must have a medium (a solid, liquid, or gas) to travel through. Sound cannot travel through a vacuum.
• Pitch: Determined by the frequency of the wave. A higher frequency creates a higher pitch.
• Loudness / Volume: Determined by the amplitude of the wave. A larger amplitude creates a louder sound.
Human Hearing Range and Ultrasound
• Normal Human Hearing Range: A healthy human ear can detect sound frequencies between \(20\text{ Hz}\) and \(20\,000\text{ Hz}\) (which can also be written as \(20\text{ kHz}\)).
• Ultrasound: Sound waves with frequencies greater than \(20\,000\text{ Hz}\) (\(20\text{ kHz}\)). These frequencies are too high for human ears to detect.
Applications of Ultrasound
1. Medicine:
• Prenatal (Foetal) Scanning: Ultrasound pulses are sent into the body and partially reflect at boundaries between different tissue densities. It is safe to use on unborn babies because ultrasound is non-ionising.
• Echocardiography: Imaging the heart.
• Destroying Kidney Stones: High-energy ultrasound vibrations break kidney stones into tiny pieces so they can pass out of the body naturally.
2. Industry:
• Non-destructive Testing: Detecting hidden cracks or internal flaws in metal pipes, structures, and railway tracks.
Echoes, Echo Sounding, and SONAR Calculations
An echo is simply a reflected sound wave. Ships and submarines use SONAR (Sound Navigation and Ranging) to measure water depth or detect submerged objects by sending ultrasound pulses to the seabed and timing their return.
The Golden Rule of Echo Calculations:
The ultrasound pulse travels to the seabed and all the way back up. That means the pulse travels double the distance (\(2d\)).
\(\text{Total Distance Travelled} = 2d = v \times t\)
To find the one-way distance (depth \(d\)):
\(d = \frac{v \times t}{2}\)
Where:
• \(d =\) depth / one-way distance to target (\(\text{m}\))
• \(v =\) speed of sound in water (\(\text{m/s}\))
• \(t =\) total two-way time for the pulse to leave and return (\(\text{s}\))
Key Takeaway: Sound is longitudinal, requires a medium, and its pitch depends on frequency while loudness depends on amplitude. Ultrasound is sound above \(20\,000\text{ Hz}\). For echo and sonar calculations, always remember to divide the two-way time or distance by \(2\)!
4. The Electromagnetic (EM) Spectrum
The Electromagnetic (EM) Spectrum is a continuous family of waves that transfer energy from a source to an absorber.
Key Properties of ALL Electromagnetic Waves
Every single wave in the electromagnetic spectrum shares these characteristics:
1. They are all transverse waves.
2. They can all travel through a vacuum (empty space—they do not need particles).
3. They all travel at the same speed in a vacuum (the speed of light): \(c = 3.0 \times 10^8\text{ m/s}\) (which is \(300\,000\,000\text{ m/s}\)).
Order of the Electromagnetic Spectrum
You must know the order of the EM 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) radiation
4. Visible light
5. Ultraviolet (UV)
6. X-rays
7. Gamma rays (\(\gamma\)) (Shortest wavelength, highest frequency, highest energy)
Mnemonic to remember the order:
"Raging Martians Invaded Venus Using X-ray Guns"
(Radio, Microwave, Infrared, Visible, Ultraviolet, X-ray, Gamma)
Visible Light
Visible light is the only part of the EM spectrum our eyes can see. It is also broken down into colours in order of decreasing wavelength / increasing frequency:
Red \(\rightarrow\) Orange \(\rightarrow\) Yellow \(\rightarrow\) Green \(\rightarrow\) Blue \(\rightarrow\) Indigo \(\rightarrow\) Violet
• Red: Longest wavelength, lowest frequency of visible light.
• Violet: Shortest wavelength, highest frequency of visible light.
Mnemonic: ROY G. BIV
Comparing SONAR and RADAR
A classic exam question asks students to distinguish between Sonar and Radar:
• SONAR: Uses ultrasound waves (longitudinal mechanical sound waves that require a liquid/substance to travel through).
• RADAR: Uses microwaves or radio waves (transverse electromagnetic waves that travel at the speed of light and can travel through air and a vacuum).
Key Takeaway: All EM waves are transverse, travel through a vacuum at \(3.0 \times 10^8\text{ m/s}\), and range from Radio waves (longest \(\lambda\), lowest \(f\)) to Gamma rays (shortest \(\lambda\), highest \(f\)).
5. Top Pitfalls & Examiner Tips
Keep these frequent exam traps in mind when revising:
1. Forgetting to Halve the Echo Time
In echo, sonar, and reflection problems, the time given is usually the round-trip time. If a question asks for the depth or distance to a barrier, divide the time by \(2\) before using distance \(= \text{speed} \times \text{time}\), or calculate total distance and divide by \(2\) at the end.
2. Measuring Amplitude Incorrectly
Never measure amplitude from crest to trough! Amplitude is strictly the distance from the equilibrium (rest) line to the peak or trough.
3. Unit Conversions
Always check your units before substituting into \(v = f \lambda\). If frequency is given in \(\text{kHz}\) or \(\text{MHz}\), or wavelength in \(\text{cm}\) or \(\text{mm}\), convert them to standard units (\(\text{Hz}\) and \(\text{m}\)) first.
4. Imprecise Wave Definitions
When defining longitudinal and transverse waves, always state that the particles vibrate / oscillate perpendicular or parallel to the direction of wave travel (energy propagation). Avoid vague phrases like "moves up and down".
5. Sound vs Light in a Vacuum
Light (an EM wave) can travel through a vacuum because it does not need particles. Sound (a mechanical wave) cannot travel through a vacuum because it requires particle vibrations.