🌊 Describe the difference between transverse and longitudinal waves in terms of the direction of oscillation relative to wave travel
🔵 Identify compressions and rarefactions in longitudinal waves and explain what they represent physically
📋 Give examples of transverse waves (light, water, S-waves) and longitudinal waves (sound, P-waves)
📺 Interpret oscilloscope traces to determine amplitude, time period, and frequency of waves
🧮 Use the wave speed equation v = f × λ with correct SI units in quantitative problems
📐 Relate the displacement-distance graph of a wave to its wavelength and amplitude
What is a Wave?
A wave is a disturbance that transfers energy from one place to another without the net transfer of matter. The particles (or fields) through which a wave travels oscillate — they move back and forth or up and down — but they do not travel with the wave. Only the energy moves through the medium.
Mechanical waves require a medium (a material substance) to travel through — e.g. sound waves, seismic waves, water waves.
Electromagnetic waves can travel through a vacuum and do not need a medium — e.g. light, radio waves, X-rays.
All waves share common properties: they have a wavelength (λ), a frequency (f), an amplitude (A), and a wave speed (v). These are related by the fundamental wave equation:
v = f × λ
Quantity
Symbol
SI Unit
Wave speed
v
m/s
Frequency
f
Hz (hertz)
Wavelength
λ
m (metres)
Amplitude
A
m (metres)
Time period
T
s (seconds)
The time period T (the time for one complete oscillation) is related to frequency by:
T = 1 ÷ f
For example, a wave with frequency 50 Hz has a time period of T = 1 ÷ 50 = 0.02 s.
Energy transferred by a wave increases with amplitude — specifically, energy is proportional to amplitude². A wave with twice the amplitude carries four times the energy.
Transverse Waves
In a transverse wave, the particles of the medium (or the fields, for EM waves) oscillate perpendicular (at right angles) to the direction in which the wave travels.
Transverse wave: oscillation is at 90° to the direction of wave propagation.
Imagine shaking one end of a rope up and down. The rope forms peaks (crests) and troughs that move along the rope, but each part of the rope only moves up and down. The wave travels horizontally but the displacement is vertical — these are perpendicular.
Examples of transverse waves:
All electromagnetic waves — light (visible, UV, IR), radio waves, microwaves, X-rays, gamma rays. These are transverse oscillations of electric and magnetic fields. They travel at 3 × 10⁸ m/s in a vacuum.
Water surface waves — the water surface moves up and down while the wave travels horizontally.
Secondary seismic waves (S-waves) — these travel through Earth's interior with particle motion perpendicular to wave travel; they cannot travel through liquids, which is evidence that Earth's outer core is liquid.
Waves on strings — e.g. guitar strings vibrating.
A transverse wave can be polarised — restricted to oscillate in one plane only. Longitudinal waves cannot be polarised. Polarisation is proof that light is a transverse wave.
On a displacement–distance graph, a transverse wave appears as a sinusoidal (S-curve) pattern. The crest is the highest point above the equilibrium and the trough is the lowest point below. The amplitude is the maximum displacement from equilibrium (not crest to trough, which is 2A).
Longitudinal Waves
In a longitudinal wave, the particles of the medium oscillate parallel to (along the same direction as) the direction of wave travel. This creates alternating regions of compression and rarefaction.
Longitudinal wave: oscillation is parallel to the direction of wave propagation.
Compressions and rarefactions are the key structural features:
Compression: a region where the particles are pushed closer together than normal. The local pressure is higher than average.
Rarefaction: a region where the particles are spread further apart than normal. The local pressure is lower than average.
Think of pushing and pulling a slinky spring along its length. When you push, coils bunch together (compression); when you pull back, coils spread apart (rarefaction). The compressions and rarefactions travel along the slinky — that is the wave.
The wavelength of a longitudinal wave is the distance from one compression to the next (or one rarefaction to the next) — i.e. the distance over which the pattern repeats.
Examples of longitudinal waves:
Sound waves — the most important example. Air molecules are pushed back and forth parallel to the direction of travel. Sound requires a medium; it cannot travel through a vacuum. Speed ≈ 340 m/s in air at room temperature.
Primary seismic waves (P-waves) — travel through solids and liquids, with particle motion parallel to travel direction. They travel faster than S-waves.
Ultrasound waves — sound waves above 20,000 Hz, used in medical imaging and sonar.
Sound cannot travel through a vacuum. This was demonstrated historically by placing a ringing bell inside a jar and pumping out the air — the sound fades as the pressure decreases, even though vibrations still occur.
Comparing Transverse and Longitudinal Waves
Feature
Transverse
Longitudinal
Oscillation direction
Perpendicular (90°) to wave travel
Parallel to wave travel
Key features
Crests and troughs
Compressions and rarefactions
Can travel in vacuum?
Yes (EM waves) / No (mechanical)
No — requires a medium
Can be polarised?
Yes
No
Examples
Light, water waves, S-waves
Sound, P-waves, ultrasound
Graph appearance
Sinusoidal (peaks and troughs)
Pressure/density variations
Both types of wave obey the same wave equation: v = f × λ, and both transfer energy without net transfer of matter.
Oscilloscope Traces
An oscilloscope is an instrument that displays electrical signals as a voltage–time graph on a screen. When connected to a microphone, it converts sound waves into electrical signals, allowing the wave pattern to be displayed and measured.
The oscilloscope screen has a grid. The key settings are:
Timebase (time/div): how many seconds (or milliseconds) each horizontal division represents. This allows you to read off the time period T.
Gain (V/div): how many volts each vertical division represents. This allows you to read off the amplitude.
Reading amplitude from an oscilloscope: count the number of vertical divisions from the equilibrium line to the peak (or trough). Multiply by the gain (V/div) setting.
Reading time period from an oscilloscope: count the number of horizontal divisions for one complete wave cycle. Multiply by the timebase (time/div) setting.
Once you have the time period T, you can calculate frequency:
f = 1 ÷ T
Interpreting changes on an oscilloscope trace:
Higher amplitude (taller wave): louder sound — more energy transferred per second.
Higher frequency (waves closer together horizontally): higher pitch sound.
Lower amplitude (shorter wave): quieter sound.
Lower frequency (waves further apart): lower pitch sound.
Although a sound wave is longitudinal, the oscilloscope converts it to a transverse-looking display. The vertical axis shows the displacement (or voltage proportional to pressure variation), and the horizontal axis shows time. This is important: the oscilloscope trace of sound is NOT showing the actual physical shape of the longitudinal wave — it is a representation of how displacement varies with time.
On an oscilloscope: amplitude ↑ means louder sound; frequency ↑ (closer peaks) means higher pitch. These two properties are independent of each other.
Example 1: A sound wave travels through air at 340 m/s and has a frequency of 850 Hz. Calculate its wavelength.
1 Write down the wave equation and the known quantities.
v = f × λ | v = 340 m/s | f = 850 Hz | λ = ?
2 Rearrange the equation to make λ the subject.
λ = v ÷ f
3 Substitute the values.
λ = 340 ÷ 850
4 Calculate and state the unit.
λ = 0.4 m
λ = 0.4 m (40 cm)
Example 2: An oscilloscope displays a sound wave. The timebase is set to 2 ms/div and the gain is set to 0.5 V/div. The wave occupies 4 divisions horizontally per complete cycle, and the peak is 3 divisions above the centre line. Find (a) the time period, (b) the frequency, and (c) the amplitude in volts.
1 Find the time period T.
T = number of divisions × timebase
T = 4 × 2 ms = 8 ms = 8 × 10⁻³ s
2 Find the frequency using f = 1 ÷ T.
f = 1 ÷ (8 × 10⁻³) = 125 Hz
3 Find the amplitude.
Amplitude = number of divisions from centre to peak × gain
A = 3 × 0.5 V = 1.5 V
(a) T = 8 × 10⁻³ s | (b) f = 125 Hz | (c) A = 1.5 V
Example 3: A radio wave has a wavelength of 3.0 m. Given that all electromagnetic waves travel at 3.0 × 10⁸ m/s in a vacuum, calculate the frequency of this radio wave. State whether it is transverse or longitudinal and give a reason.
1 Write the wave equation and identify known quantities.
v = f × λ | v = 3.0 × 10⁸ m/s | λ = 3.0 m | f = ?
4 Classify the wave.
Radio waves are part of the electromagnetic spectrum. All EM waves are transverse — the electric and magnetic fields oscillate perpendicular to the direction of travel. They can also be polarised, confirming they are transverse.
f = 1.0 × 10⁸ Hz (100 MHz) — Transverse wave (all EM waves are transverse)
Example 4: Two oscilloscope traces A and B are compared. Trace A has peaks that are 2 divisions tall and 5 divisions apart (per cycle). Trace B has peaks that are 4 divisions tall and 2.5 divisions apart (per cycle). The timebase is 1 ms/div. Describe the difference in the sounds represented by A and B.
1 Find the time period for each trace.
T_A = 5 × 1 ms = 5 ms = 5 × 10⁻³ s
T_B = 2.5 × 1 ms = 2.5 ms = 2.5 × 10⁻³ s
2 Find the frequency for each trace.
f_A = 1 ÷ (5 × 10⁻³) = 200 Hz
f_B = 1 ÷ (2.5 × 10⁻³) = 400 Hz
3 Compare amplitudes.
Amplitude of A = 2 divisions | Amplitude of B = 4 divisions
Amplitude of B is twice that of A.
4 Describe the sounds.
Trace B has a higher frequency (400 Hz vs 200 Hz) → higher pitch.
Trace B has a larger amplitude (4 div vs 2 div) → louder sound.
Sound B is louder (larger amplitude) AND higher pitched (higher frequency, shorter time period) than sound A.
Question 1: In a transverse wave, how does the direction of particle oscillation relate to the direction of wave travel?
Question 2: Which of the following is a longitudinal wave?
Question 3: A sound wave has a frequency of 440 Hz and a wave speed of 330 m/s. Calculate the wavelength. Enter your answer in metres to 2 decimal places.
Question 4: An oscilloscope has a timebase of 5 ms/div. A complete wave cycle spans 4 horizontal divisions. What is the frequency of the wave?
Question 5: In a longitudinal wave, what is a compression?
Challenge 1 (6 marks): A student uses a microphone and oscilloscope to compare two musical notes, X and Y.
Note X: time period = 4 ms, amplitude = 3 divisions on screen.
Note Y: time period = 2 ms, amplitude = 6 divisions on screen.
(a) Calculate the frequency of both notes. (b) Describe the differences in how notes X and Y would sound. (c) Explain why the oscilloscope trace looks like a transverse wave even though sound is longitudinal.
(b) Note Y has twice the frequency of X → Note Y has a higher pitch. Note Y has twice the amplitude of X → Note Y is louder (more energy transferred per second).
(c) The oscilloscope converts the pressure variations of the longitudinal sound wave into an electrical voltage signal. The microphone diaphragm vibrates with the compressions and rarefactions, producing a varying voltage. The oscilloscope plots this voltage against time, producing a sinusoidal trace. This trace represents the variation in displacement/pressure over time — it is NOT showing the physical shape of the sound wave in the air. The wave shown is transverse-looking because the y-axis (displacement) is perpendicular to the x-axis (time/direction of travel shown).
Challenge 2 (5 marks): A seismologist detects both P-waves and S-waves from an earthquake. P-waves travel at 8000 m/s and have a wavelength of 400 m. S-waves travel at 4500 m/s.
(a) Calculate the frequency of the P-waves. (b) If S-waves have the same frequency, calculate the wavelength of the S-waves. (c) Explain why S-waves cannot pass through Earth's outer core, and what this tells us about the outer core.
(a) f = v ÷ λ = 8000 ÷ 400 = 20 Hz
(b) λ_S = v_S ÷ f = 4500 ÷ 20 = 225 m
(c) S-waves are transverse waves — particles oscillate perpendicular to the direction of travel. Transverse mechanical waves require a medium with shear strength (resistance to sideways deformation). Liquids and gases have no shear strength, so transverse waves cannot propagate through them. Since S-waves are not detected on the opposite side of Earth from an earthquake (in the S-wave shadow zone), this is evidence that Earth's outer core is liquid.
Challenge 3 (4 marks): A student claims: "Longitudinal waves transfer more energy than transverse waves because the particles actually travel with the wave." Identify two errors in this statement and correct them.
Error 1: "Longitudinal waves transfer more energy than transverse waves" — This is incorrect. Both types of wave can transfer any amount of energy depending on their amplitude and frequency. Neither type is inherently more energetic than the other. The energy carried by a wave depends on its amplitude squared, not on whether it is transverse or longitudinal.
Error 2: "particles actually travel with the wave" — This is incorrect for ALL waves (both transverse and longitudinal). In any wave, the particles oscillate about their equilibrium positions — they do not travel with the wave. It is energy that is transferred, not matter. In a longitudinal wave, particles oscillate back and forth parallel to wave travel, but they return to their original positions — they do not undergo net displacement in the direction of travel.
Challenge 4 (6 marks): An oscilloscope displays the trace of an ultrasound pulse used in a medical scan. The timebase is set to 10 μs/div (10 × 10⁻⁶ s/div) and the gain is 0.2 V/div. The complete cycle spans 2.5 divisions horizontally, and the peak is 4 divisions above the midline. The speed of ultrasound in tissue is 1500 m/s.
(a) Find the time period of the ultrasound. (b) Find the frequency. (c) Find the wavelength in tissue. (d) State one medical application of ultrasound and explain why ultrasound is preferred over X-rays for this application.
(a) T = 2.5 × 10 × 10⁻⁶ = 2.5 × 10⁻⁵ s (25 μs)
(b) f = 1 ÷ T = 1 ÷ (2.5 × 10⁻⁵) = 4 × 10⁴ Hz = 40 kHz
(c) λ = v ÷ f = 1500 ÷ (4 × 10⁴) = 0.0375 m = 3.75 cm
(d) Application: foetal scanning during pregnancy (or kidney stone detection, muscle imaging). Ultrasound is preferred over X-rays because ultrasound is non-ionising — it does not damage DNA or cells, making it safe for imaging a developing foetus. X-rays are ionising radiation which can cause cell damage and increase cancer risk, so they are avoided where possible, especially for vulnerable patients such as pregnant women and young children.