Transverse & longitudinal waves
By the end of this topic you'll tell the two wave types apart, name the four properties of a wave, and use T = 1/f without blinking.
Part 1Two ways a wave can wobble
A wave transfers energy from one place to another without transferring matter. That last bit matters: when a wave passes through water, the water itself doesn't travel along — it just bobs up and down while the energy moves on.
In a transverse wave, the oscillations are at 90° (perpendicular) to the direction the wave travels. Ripples on water, waves on a rope, and all electromagnetic waves are transverse.
In a longitudinal wave, the oscillations are parallel to the direction of travel — back and forth along the same line. This makes regions of compression (squashed together) and rarefaction (spread out). Sound is the key example.
⚠ Watch out — sound is longitudinal
A classic trap: sound waves are longitudinal, not transverse, even though they're drawn as wiggly lines on an oscilloscope. The oscilloscope shows pressure changing over time — the real air particles move back and forth, making compressions and rarefactions. And remember: in both wave types only energy moves along, the medium just oscillates in place.
Which statement about a sound wave travelling through air is correct?
- AIt is transverse, and the air moves along with it
- BIt is longitudinal; air particles oscillate parallel to the direction of travel
- CIt is transverse; air particles oscillate at 90° to travel
- DIt is longitudinal, and the air is carried from speaker to ear
Show answer
Part 2The properties of a wave
Every wave can be described by the same four quantities. Learn them and their units:
The four wave properties
- Amplitude
- The maximum displacement from the rest (undisturbed) position. Bigger amplitude = more energy. Unit: metres (m).
- Wavelength
- The distance from one point on a wave to the same point on the next — e.g. crest to crest. Symbol λ. Unit: metres (m).
- Frequency
- The number of complete waves passing a point each second. Unit: hertz (Hz). 1 Hz = 1 wave per second.
- Period (T)
- The time for one complete wave to pass. Unit: seconds (s).
Equation
- T = 1 / f recall
- period (s) = 1 ÷ frequency (Hz). Period and frequency are reciprocals — fast waves (high f) have a short period.
Worked example — period from frequency
A water wave has a frequency of 5 Hz. Calculate its period.
⚠ Watch out — amplitude is from the middle
Amplitude is measured from the rest position to the crest (or to the trough) — it is not the full distance from crest to trough. The full crest-to-trough height is twice the amplitude. Mixing these up loses easy marks.
A wave has a period of 0.04 s. What is its frequency?
- A0.04 Hz
- B4 Hz
- C25 Hz
- D250 Hz
Show answer
What does a wave transfer, and what does it not transfer?
A wave transfers energy from place to place without transferring matter — the medium just oscillates.Give the difference between a transverse and a longitudinal wave.
In a transverse wave the oscillations are perpendicular (90°) to the travel; in a longitudinal wave they are parallel to the travel (making compressions and rarefactions).State one example of each wave type.
Transverse: ripples on water / waves on a rope / any EM wave. Longitudinal: sound waves.Define amplitude.
The maximum displacement of a point on the wave from its rest position.A wave has a frequency of 50 Hz. Calculate its period.
T = 1 ÷ f = 1 ÷ 50 = 0.02 s.
Wave speed
One equation to recall, the units that catch people out, and the required practical for measuring waves on water and on a string.
Part 1The wave equation
The wave speed is how fast the energy moves through the medium. It links the wavelength and frequency in the most-used equation in P6:
Equation
- v = f λ recall
- wave speed (m/s) = frequency (Hz) × wavelength (m). You must memorise this one — it isn't on the equation sheet.
Worked example — speed of a sound wave
A sound wave has a frequency of 170 Hz and a wavelength of 2.0 m. Calculate the wave speed.
⚠ Watch out — convert to metres and hertz
Wavelength must be in metres and frequency in hertz before you multiply. A wavelength given in centimetres (e.g. 25 cm) must become 0.25 m first. A frequency in kHz must become Hz (1 kHz = 1000 Hz). Getting the units right is usually the whole battle.
Worked example — finding a wavelength
A wave on a string travels at 12 m/s with a frequency of 30 Hz. Find its wavelength.
A water wave has a wavelength of 0.5 m and a frequency of 4 Hz. What is its speed?
- A8 m/s
- B0.125 m/s
- C2 m/s
- D4.5 m/s
Show answer
Part 2Measuring waves
The required practical has two parts — measuring a wave on water in a ripple tank, and measuring a wave on a stretched string. In both, you find the frequency and wavelength, then use v = f λ to get the speed.
Measuring frequency, wavelength and speed of waves
Aim: measure the frequency, wavelength and speed of waves in a ripple tank and on a stretched string.
Ripple tank (water waves):
- Set a signal generator and dipper going to make waves of a steady frequency; read the frequency off the generator.
- Use a lamp above the tank to project the wave shadows onto the bench below.
- Measure the length of, say, 10 wavelengths with a ruler and divide by 10 to find one wavelength (this reduces the percentage error).
- Calculate the speed: v = f × λ
Stretched string:
- Fix one end of a string and pass it over a pulley to a hanging mass; drive it with a vibration generator at a known frequency.
- Adjust the frequency until you get a clear standing wave with whole loops.
- Measure the length of the loops and work out the wavelength (one full wave = two loops).
- Calculate the speed with v = f × λ
Control / improve: measuring several wavelengths at once and dividing reduces the percentage uncertainty; a strobe or freezing the image makes the moving wave easier to measure accurately.
In a ripple tank, 8 wavelengths measure 24 cm and the generator reads 6 Hz. What is the wave speed?
- A0.18 m/s
- B1.44 m/s
- C18 m/s
- D0.5 m/s
Show answer
Write the wave equation and state whether you must recall it.
v = f λ (wave speed = frequency × wavelength). Yes — recall it; it's not on the sheet.A wave has frequency 25 Hz and wavelength 4 m. Find its speed.
v = f λ = 25 × 4 = 100 m/s.A wave travels at 6 m/s with a wavelength of 0.3 m. Find its frequency.
f = v ÷ λ = 6 ÷ 0.3 = 20 Hz.In the required practical, why measure 10 wavelengths and divide by 10?
It reduces the percentage uncertainty in the measurement compared with measuring a single wavelength.How is the frequency found in the ripple-tank experiment?
It is read directly off the signal generator driving the dipper.
The electromagnetic spectrum
Seven groups, one running order to learn for life, and the three facts that hold them all together.
Part 1One family of waves
Electromagnetic (EM) waves are transverse waves that all travel at the same speed through a vacuum (or through air) — the speed of light, 3 × 10⁸ m/s. They don't need a medium, which is how light reaches us from the Sun across empty space.
They form a continuous spectrum grouped into seven bands by their wavelength and frequency. You must know them in order:
The seven groups (long λ / low f → short λ / high f)
- Radio waves
- Longest wavelength, lowest frequency, lowest energy.
- Microwaves
- Shorter than radio.
- Infrared
- Felt as heat / radiated by warm objects.
- Visible light
- The only part our eyes detect (red → violet).
- Ultraviolet
- Just beyond violet; starts to be harmful.
- X-rays
- Very short wavelength, high frequency.
- Gamma rays
- Shortest wavelength, highest frequency, highest energy.
A memory trick for the order: Rich Men In Vegas Use Xpensive Gadgets. As you go from radio to gamma, the wavelength gets shorter, the frequency gets higher, and the energy increases.
⚠ Watch out — "same speed" only in a vacuum
All EM waves travel at the same speed in a vacuum (and very nearly so in air). They do not all have the same wavelength or frequency — those are exactly what change across the spectrum. Also remember the whole spectrum is transverse; none of it is longitudinal.
Which group has the highest frequency and shortest wavelength?
- ARadio waves
- BVisible light
- CGamma rays
- DMicrowaves
Show answer
List the seven EM groups in order from longest to shortest wavelength.
Radio, microwaves, infrared, visible light, ultraviolet, X-rays, gamma rays.Are EM waves transverse or longitudinal?
All EM waves are transverse.What do all EM waves have in common in a vacuum?
They all travel at the same speed (the speed of light, 3 × 10⁸ m/s).Which part of the spectrum can the human eye detect?
Only visible light.Going from radio to gamma, what happens to wavelength and energy?
Wavelength decreases; frequency and energy increase.
Uses & dangers of EM waves
What each group is used for, why the high-energy end is dangerous, and what "ionising" really means.
Part 1What each group is used for
Each group's uses follow from its properties. Learn at least one use per group:
Uses across the spectrum
- Radio waves
- Television and radio broadcasting; long-distance communication.
- Microwaves
- Satellite communications and cooking food (microwave ovens).
- Infrared
- Electrical heaters, cooking food, and infrared cameras (thermal imaging); also short-range communication like remote controls.
- Visible light
- Fibre-optic communication and photography / seeing.
- Ultraviolet
- Energy-efficient lamps, sun tanning, and security marking.
- X-rays
- Medical imaging — seeing bones and internal structures.
- Gamma rays
- Sterilising medical equipment and food; treating cancer (radiotherapy).
Part 2Ionising radiation & risk
The danger of an EM wave depends on its energy, which rises towards the gamma end. The three highest-energy groups — ultraviolet, X-rays and gamma rays — carry enough energy to be ionising: they can knock electrons off atoms inside your cells.
Ionising radiation can damage cells and DNA, which can cause mutations that may lead to cancer. Ultraviolet from the Sun damages skin cells (causing ageing and skin cancer) and can damage the eyes — which is why sun cream and sunglasses help. X-rays and gamma rays can pass deep into the body, so doses are kept low and medical staff are shielded.
⚠ Watch out — only the high-energy end ionises
Radio, microwaves, infrared and visible light are not ionising at the levels we meet them — they don't have enough energy. The ionising, more dangerous waves are UV, X-rays and gamma. Don't claim a radio wave can give you cancer by ionising your cells; it can't.
How to answer a "use AND danger" question
"State a use of ultraviolet and one danger of it." (How to structure it.)
Which set of EM waves is ionising and so carries the greatest risk to health?
- ARadio, microwaves, infrared
- BInfrared, visible light, ultraviolet
- CUltraviolet, X-rays, gamma rays
- DMicrowaves, X-rays, gamma rays
Show answer
Give one use of microwaves and one use of infrared.
Microwaves: satellite communication or cooking food. Infrared: heaters, cooking, thermal imaging, or remote controls.State a use of X-rays and a use of gamma rays.
X-rays: medical imaging of bones. Gamma rays: sterilising equipment or treating cancer.What does "ionising" mean?
The radiation has enough energy to knock electrons off atoms, which can damage cells and DNA.Which three EM groups are ionising?
Ultraviolet, X-rays and gamma rays.Give one danger of over-exposure to ultraviolet.
Damage to skin cells (premature ageing and skin cancer) and damage to the eyes.
Reflection & refraction
What a wave does when it hits a boundary — bounce off, or bend through — and why the bending happens.
Part 1Reflection
When a wave hits a boundary between two materials it can be reflected, absorbed, or transmitted (pass through). Reflection is when the wave bounces off the surface.
For reflection we measure angles from the normal — a line drawn at 90° to the surface where the ray hits. The rule is simple: the angle of incidence equals the angle of reflection. Both angles are measured between the ray and the normal, not the surface.
⚠ Watch out — measure from the normal
Angles of incidence and reflection are always measured between the ray and the normal, not the surface. A common slip is measuring from the surface itself, which gives the wrong value (it's 90° minus the correct angle).
Part 2Refraction
Refraction is the change in direction of a wave as it crosses a boundary into a different material — for example, light passing from air into glass. The wave bends because its speed changes in the new material, while its frequency stays the same (so the wavelength changes).
The rule of thumb: when a wave slows down (entering a denser material like glass), it bends towards the normal. When it speeds up (coming back out into air), it bends away from the normal. If it hits the boundary straight on (along the normal), it doesn't bend at all.
⚠ Watch out — refraction doesn't change frequency
When a wave refracts, its speed and wavelength change but its frequency stays the same. The wave bends only because the speed changes. If a wave hits the boundary along the normal (0° incidence), it slows down but carries straight on — no bending.
A ray of light passes from air into a glass block at an angle. What happens?
- AIt speeds up and bends away from the normal
- BIt slows down and bends towards the normal
- CIts frequency increases as it enters the glass
- DIt carries straight on without changing direction
Show answer
Name the three things that can happen to a wave at a boundary.
It can be reflected, absorbed, or transmitted (pass through, often refracting).What is the "normal" and why does it matter?
A line drawn at 90° to the surface where the ray hits. All angles of incidence, reflection and refraction are measured from the normal.State the law of reflection.
The angle of incidence equals the angle of reflection (both measured from the normal).Why does a wave refract (bend) at a boundary?
Because its speed changes in the new material. Its frequency stays the same, so the wavelength changes too.Light goes from glass into air. Which way does it bend?
It speeds up, so it bends away from the normal.