Properties of waves

Q: Do I get the wave formulae on the Edexcel IGCSE Physics formula sheet?

No, you must recall both and from memory, as they are not provided on the formula sheet.

Edexcel International GCSE Physics· 3.1 - 3.9· 15 min read

1. Wave Types and Core Properties★☆☆☆☆⏱ 3 min

🚫 No Calculator

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
1. Sound travels via vibrations of air particles parallel to its direction of travel, with compressions and rarefactions, so it is a longitudinal wave.

2. Key Wave Terms, Units and Formulae★★☆☆☆⏱ 4 min

✓ Calculator OK

📘 Definition

Core Wave Quantities

A, \lambda, f, T

Amplitude (A): Maximum displacement from rest position, units metres (m). Wavelength ( $λ$ ): 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.

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
1. Use $v = f λ$ to find wave speed:
4
$v = 50 \times 1.5 = 75 \text{ m/s}$

3. Contextual Wave Calculations★★★☆☆⏱ 4 min

✓ Calculator OK

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 $3 \times 1 0^{8}$ 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
1. Rearrange $v = f λ$ to solve for wavelength:
4
$\lambda = \frac{v}{f}$
5
1. Substitute values ( $v = 3 \times 1 0^{8}$ m/s for EM waves):
6
$\lambda = \frac{3 \times 10^8}{9.5 \times 10^7} \approx 3.16 \text{ m}$

✓ Quick check

What is the period of a 200 Hz sound wave?
- A) 0.005 s
- B) 0.05 s
- C) 200 s
Reveal answer
A —
Use $T = 1/ f = 1/200 = 0.005$ s. Remember period is the inverse of frequency.
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
Reveal answer
C —
Rearrange $v = f λ$ to $f = v / λ = 340/0.17 = 2000$ Hz.

4. Doppler Effect and Core Wave Behaviours★★☆☆☆⏱ 3 min

🚫 No Calculator

📘 Definition

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
1. Shorter observed wavelength leads to higher observed frequency, so the siren sounds higher pitched.
3
1. When moving away: Wavefronts stretch out behind the source, leading to longer observed wavelength and lower observed frequency, so the siren sounds lower pitched.

5. Common Pitfalls

Wrong move:

Mixing up oscillation directions for transverse and longitudinal waves

Why:

This is a common 1-2 mark exam question, mixing the two loses easy marks

Correct move:

Remember transverse = perpendicular, longitudinal = parallel; use examples (EM = transverse, sound = longitudinal) to check your answer

Wrong move:

Using non-SI units directly in wave calculations (e.g. kHz, cm)

Why:

Wave formulae only give correct answers when using SI units (Hz, m, m/s)

Correct move:

Convert all units to SI first: multiply kHz by 1000 to get Hz, multiply cm by 0.01 to get m

Wrong move:

Stating that waves transfer matter as they travel

Why:

This is a common misconception tested in multiple choice questions

Correct move:

Recall that waves only transfer energy and information, with no net movement of matter particles

Wrong move:

Using $f = T$ instead of $f = 1/ T$ for frequency calculations

Why:

The formula is not provided on the formula sheet, so misremembering it leads to wrong answers

Correct move:

Recall frequency is the number of waves per second, so divide 1 by the time for one wave (period) to get frequency

Wrong move:

Claiming the Doppler effect changes the frequency emitted by the source

Why:

Examiners regularly test that only observed frequency changes, not source frequency

Correct move:

Clarify the source emits a constant frequency, only the observed frequency and wavelength change with relative movement

6. Quick Reference Cheatsheet

Quantity	Symbol	Unit	Formula/Definition
Amplitude	A	m	Max displacement from rest position
Wavelength	$λ$	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	$v = f \times λ$
Transverse Wave			Oscillations perpendicular to energy transfer
Longitudinal Wave			Oscillations parallel to energy transfer
Doppler (Approaching Source)			Observed f higher, $λ$ shorter
Doppler (Receding Source)			Observed f lower, $λ$ longer

7. Frequently Asked

Do I get the wave formulae on the Edexcel IGCSE Physics formula sheet?

No, you must recall both $v = f \times λ$ and $f = 1/ T$ from memory, as they are not provided on the formula sheet.

Do I need to calculate Doppler shift values for this topic?

No, this topic only requires a qualitative explanation of the Doppler effect. Quantitative red-shift calculations are part of the separate astrophysics unit.

Going deeper

syllabusEdexcel 4PH1 Full SpecificationRefer to Section 3 for full waves unit guidance

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.