# Properties of waves

> Edexcel International GCSE Physics · 4PH1 2017
> Source: https://www.owlsprep.com/study/edexcel-igcse-physics-s3-properties-of-waves/

This guide covers all core properties of waves required for Edexcel IGCSE Physics (4PH1) points 3.1 to 3.9, including wave types, key definitions, calculations, the Doppler effect, and basic wave behaviours.

**Prerequisites:** [Basic SI unit conversion skills](https://www.owlsprep.com/study/edexcel-igcse-physics-s1-si-units/)

## Learning objectives

- Distinguish between transverse and longitudinal waves and their real-world examples
- Define key wave terms including amplitude, wavelength, frequency, period and wavefront
- Recall and apply the wave speed and frequency-period formulae for calculation questions
- Explain the qualitative Doppler effect and core wave behaviours (reflection, refraction)

## Wave Types and Core Properties

All waves transfer energy and information without transferring any net matter. For example, a floating cork will bob up and down as a water wave passes, but will not be carried to the shore by the wave.

- **Transverse waves**: Oscillations are *perpendicular* to the direction of energy transfer. Examples include all electromagnetic waves, water ripples, and waves on a stretched string.
- **Longitudinal waves**: Oscillations are *parallel* to the direction of energy transfer, made of alternating compressions (high particle density) and rarefactions (low particle density). Examples include sound waves and seismic P-waves.

**Worked example:** Classify a light wave and a sound wave, giving a reason for each classification.

1. 1. Light is an electromagnetic wave: its oscillations of electric and magnetic fields are perpendicular to its direction of travel, so it is a transverse wave.
2. 2. Sound travels via vibrations of air particles parallel to its direction of travel, with compressions and rarefactions, so it is a longitudinal wave.

> **Exam tip**
>
> Always give a named example of each wave type when asked in exams, as this is a common 2-mark question. Memorize EM waves as transverse and sound as longitudinal for quick marks.

*Calculator:* forbidden

## Key Wave Terms, Units and Formulae

**Core Wave Quantities** — Amplitude (A): Maximum displacement from rest position, units metres (m). Wavelength ($\lambda$): Distance between two adjacent in-phase points, units metres (m). Frequency (f): Number of waves per second, units hertz (Hz). Time period (T): Time for one complete wave, units seconds (s). Wavefront: Line joining points oscillating in phase.

*Notation:* A, \lambda, f, T

*Example:* A 10 Hz sound wave has 10 complete waves passing a point every second, so its time period is 0.1 s.

You must recall two formulae for this topic, as they are not provided on the exam formula sheet:

$$v = f \times \lambda$$

$$f = \frac{1}{T}$$

**Worked example:** Calculate the frequency of a wave with a time period of 0.02 s, then find its wave speed if its wavelength is 1.5 m.

1. 1. Use $f = 1/T$ to find frequency:
2. $$f = \frac{1}{0.02} = 50 \text{ Hz}$$
3. 2. Use $v = f\lambda$ to find wave speed:
4. $$v = 50 \times 1.5 = 75 \text{ m/s}$$

> **warning**
>
> Always convert units to SI before calculating: multiply kHz by 1000 to get Hz, multiply cm by 0.01 to get m, otherwise you will get incorrect answers.

*Calculator:* allowed

## Contextual Wave Calculations

You will be expected to apply the wave formulae across different contexts, including sound waves and electromagnetic waves. The speed of all electromagnetic waves in a vacuum is $3 \times 10^8$ m/s, which you can use for all EM wave calculation questions.

**Worked example:** A FM radio wave has a frequency of 95 MHz. Calculate its wavelength.

1. 1. Convert frequency to SI units (Hz):
2. $$95 \text{ MHz} = 95 \times 10^6 = 9.5 \times 10^7 \text{ Hz}$$
3. 2. Rearrange $v = f\lambda$ to solve for wavelength:
4. $$\lambda = \frac{v}{f}$$
5. 3. Substitute values ($v = 3 \times 10^8$ m/s for EM waves):
6. $$\lambda = \frac{3 \times 10^8}{9.5 \times 10^7} \approx 3.16 \text{ m}$$

**Check your understanding**

1. What is the period of a 200 Hz sound wave?

   - A) 0.005 s
   - B) 0.05 s
   - C) 200 s

   *Why:* Use $T = 1/f = 1/200 = 0.005$ s. Remember period is the inverse of frequency.

2. A sound wave travels at 340 m/s with a wavelength of 0.17 m. What is its frequency?

   - A) 20 Hz
   - B) 200 Hz
   - C) 2000 Hz

   *Why:* Rearrange $v = f\lambda$ to $f = v/\lambda = 340 / 0.17 = 2000$ Hz.

*Calculator:* allowed

## Doppler Effect and Core Wave Behaviours

**Doppler Effect** — The observed change in frequency and wavelength of a wave when its source moves relative to a stationary observer. The frequency emitted by the source itself does not change.

*Example:* An ambulance siren sounds higher pitched when approaching you, and lower pitched when driving away from you.

- Source moving *towards* observer: Wavefronts bunch up in front of the source, observed wavelength is shorter, observed frequency is higher.
- Source moving *away from* observer: Wavefronts stretch out behind the source, observed wavelength is longer, observed frequency is lower.

All waves (both transverse and longitudinal) can be reflected (bounce off a surface) and refracted (change speed and direction when moving between two different mediums).

**Worked example:** Explain why a stationary observer hears a higher frequency siren when an ambulance approaches, and lower frequency when it moves away.

1. 1. When approaching: The ambulance moves towards the observer, so sound wavefronts bunch up in front of the source.
2. 2. Shorter observed wavelength leads to higher observed frequency, so the siren sounds higher pitched.
3. 3. When moving away: Wavefronts stretch out behind the source, leading to longer observed wavelength and lower observed frequency, so the siren sounds lower pitched.

> **Exam tip**
>
> You will never be asked to calculate Doppler shift values for this topic, only explain the qualitative effect. Always link frequency changes to wavelength changes to get full marks.

*Calculator:* forbidden

## Common pitfalls

- **Wrong:** Mixing up oscillation directions for transverse and longitudinal waves
  - Why it fails: This is a common 1-2 mark exam question, mixing the two loses easy marks
  - Correct: Remember transverse = perpendicular, longitudinal = parallel; use examples (EM = transverse, sound = longitudinal) to check your answer
- **Wrong:** Using non-SI units directly in wave calculations (e.g. kHz, cm)
  - Why it fails: Wave formulae only give correct answers when using SI units (Hz, m, m/s)
  - Correct: Convert all units to SI first: multiply kHz by 1000 to get Hz, multiply cm by 0.01 to get m
- **Wrong:** Stating that waves transfer matter as they travel
  - Why it fails: This is a common misconception tested in multiple choice questions
  - Correct: Recall that waves only transfer energy and information, with no net movement of matter particles
- **Wrong:** Using $f = T$ instead of $f = 1/T$ for frequency calculations
  - Why it fails: The formula is not provided on the formula sheet, so misremembering it leads to wrong answers
  - Correct: Recall frequency is the number of waves per second, so divide 1 by the time for one wave (period) to get frequency
- **Wrong:** Claiming the Doppler effect changes the frequency emitted by the source
  - Why it fails: Examiners regularly test that only observed frequency changes, not source frequency
  - Correct: Clarify the source emits a constant frequency, only the observed frequency and wavelength change with relative movement

## Cheatsheet

| Quantity | Symbol | Unit | Formula/Definition |
| --- | --- | --- | --- |
| Amplitude | A | m | Max displacement from rest position |
| Wavelength | $\lambda$ | m | Distance between two adjacent in-phase points |
| Frequency | f | Hz | Number of waves per second; $f = 1/T$ |
| Time Period | T | s | Time for one complete wave; $T = 1/f$ |
| Wave Speed | v | m/s | $v = f \times \lambda$ |
| Transverse Wave | - | - | Oscillations perpendicular to energy transfer |
| Longitudinal Wave | - | - | Oscillations parallel to energy transfer |
| Doppler (Approaching Source) | - | - | Observed f higher, $\lambda$ shorter |
| Doppler (Receding Source) | - | - | Observed f lower, $\lambda$ longer |

## What's next

Now that you have mastered core wave properties, you are ready to progress to the remaining sub-topics in the Edexcel IGCSE Physics waves unit. Next, you will learn about the full electromagnetic spectrum, including its ordering, common uses, and associated safety risks, as well as how EM wave properties apply to real-world technologies. Following that, you will explore detailed wave behaviours including the laws of reflection and refraction, ray diagrams, total internal reflection, and specific properties of sound waves. This foundational knowledge will also be critical when you later study astrophysics topics, including the Doppler red-shift evidence for the expansion of the universe. Make sure you memorize the two wave formulae and unit conversion rules, as they will appear frequently across all these subsequent topics.

---

From [OwlsPrep](https://www.owlsprep.com) — free study guides for A-Level, IB, AP and IGCSE, written against the official syllabus. Canonical page: https://www.owlsprep.com/study/edexcel-igcse-physics-s3-properties-of-waves/