Unit A2 4: Sound and Light — Chapter 11: Waves
Welcome to your study notes for Waves! Whether you are already confident in physics or find equations and wave diagrams a little daunting, don't worry. Waves are simply the way energy travels from one place to another. By breaking down the core definitions, formulas, and principles step by step, you will master everything required for your CCEA A2 Life and Health Sciences exam.
1. What is a Wave? Transverse vs. Longitudinal
A wave is a disturbance that transfers energy from one point to another without transferring matter. In physics, we classify waves based on the direction in which their oscillations (vibrations) occur relative to the direction that energy is moving.
Transverse Waves
• Definition: In a transverse wave, the oscillations are perpendicular (\(90^\circ\)) to the direction of energy transfer.
• Example: Light waves (and all other electromagnetic waves).
• Everyday Analogy: Imagine wiggling a rope up and down. The wave ripples forward along the rope, but the rope itself only moves up and down.
Longitudinal Waves
• Definition: In a longitudinal wave, the oscillations are parallel to the direction of energy transfer.
• Example: Sound waves.
• Everyday Analogy: Imagine pushing and pulling a stretched Slinky spring back and forth. The compressions travel forward in the same direction as your hand's push.
Memory Trick:
• Transverse = T-shaped / perpendicular (\(\perp\)).
• Longitudinal = Lines side-by-side / parallel (\(\parallel\)).
Key Takeaway: Always state whether vibrations are perpendicular (transverse) or parallel (longitudinal) to the direction of energy transfer to gain full marks in exam definitions.
2. Key Wave Properties and Formulae
To describe waves mathematically, we use a few standard quantities:
• Wavelength (\(\lambda\)): The distance between two successive identical points on a wave, such as from crest to crest or trough to trough. Measured in metres (\(\text{m}\)).
• Frequency (\(f\)): The number of complete wave cycles passing a point per second. Measured in Hertz (\(\text{Hz}\)).
• Time Period (\(T\)): The time taken for one complete wave cycle to pass a fixed point. Measured in seconds (\(\text{s}\)).
• Wave Speed (\(v\)): The distance travelled by the wave per unit time. Measured in metres per second (\(\text{m/s}\)).
The Key Formulae
1. Time Period and Frequency:
\(T = \frac{1}{f}\) or \(f = \frac{1}{T}\)
2. The Wave Equation:
\(v = f \lambda\)
Where:
• \(v\) = wave speed in \(\text{m/s}\)
• \(f\) = frequency in \(\text{Hz}\)
• \(\lambda\) = wavelength in \(\text{m}\)
Step-by-Step Worked Example
Question: A medical ultrasound wave travels through human soft tissue at a speed of \(1540 \text{ m/s}\). If the frequency of the ultrasound is \(2.0 \text{ MHz}\), calculate its wavelength.
Step 1: Identify the given values and check your units!
• Speed (\(v\)) = \(1540 \text{ m/s}\)
• Frequency (\(f\)) = \(2.0 \text{ MHz} = 2.0 \times 10^6 \text{ Hz}\)
Step 2: Rearrange the wave equation for \(\lambda\):
\(v = f \lambda \implies \lambda = \frac{v}{f}\)
Step 3: Substitute the values into the formula:
\(\lambda = \frac{1540}{2.0 \times 10^6} = 7.7 \times 10^{-4} \text{ m}\) (or \(0.77 \text{ mm}\))
Key Takeaway: Before putting numbers into \(v = f \lambda\), always convert prefixes like \(\text{kHz}\) (\(\times 10^3\)), \(\text{MHz}\) (\(\times 10^6\)), or \(\text{nm}\) (\(\times 10^{-9}\)) back into standard base units (\(\text{Hz}\) and \(\text{m}\)).
3. Superposition and Interference
What happens when two or more waves meet as they travel through the same medium? They pass through each other and combine!
The Principle of Superposition
The principle of superposition states that when two or more waves overlap, the total displacement at any point is equal to the vector sum of the individual displacements of the waves at that point.
Constructive vs. Destructive Interference
Interference is the overall effect observed when two overlapping waves superpose.
• Constructive Interference: Occurs when two waves meet in phase (e.g., crest meets crest or trough meets trough). Their displacements reinforce each other, resulting in a wave of larger amplitude.
• Destructive Interference: Occurs when two waves meet in antiphase (e.g., a crest meets a trough). Their displacements cancel each other out, resulting in a wave of smaller or zero amplitude.
Coherent Sources
To produce a stable, observable interference pattern, the wave sources must be coherent.
Condition for Coherence: Two wave sources are coherent if they have the same frequency (and wavelength) and maintain a constant phase difference.
Key Takeaway: "Coherent" does not simply mean "in phase" — it means the phase difference between the sources does not change over time.
4. Common Exam Pitfalls to Avoid
• Forgetting Unit Conversions: Make sure to convert \(\text{kHz}\) to \(\text{Hz}\) (\(\times 10^3\)) and \(\text{nm}\) to \(\text{m}\) (\(\times 10^{-9}\)) before using \(v = f \lambda\).
• Vague Definitions: Saying a transverse wave "moves up and down" loses marks. You must explicitly state: oscillations are perpendicular to the direction of energy transfer.
• Misunderstanding Coherence: Remember both parts of the definition: (1) same frequency and (2) constant phase difference.
5. Quick Summary Checklist
Before moving on to the next chapter, check that you can:
• Define transverse and longitudinal waves and give an example of each.
• State and use the formulas \(T = \frac{1}{f}\) and \(v = f \lambda\).
• Explain the difference between constructive and destructive interference.
• State the two conditions required for wave sources to be coherent.