O-Level Pure Physics: Waves, Sound & the EM Spectrum — From a Vibrating String to Gamma Rays

Why Waves, Sound & the EM Spectrum Matter in the Exam

Waves run quietly through a large part of the O-Level Pure Physics syllabus. The same ideas — amplitude, wavelength, frequency, period, and wave speed — reappear when you study general wave properties, sound, and the electromagnetic (EM) spectrum. Get the core definitions secure and one set of skills earns you marks across three separate topics.

Most lost marks here are not from difficult physics. They come from mixing up frequency with speed, misreading amplitude and wavelength off a graph, claiming sound can travel through a vacuum, or scrambling the order of the EM spectrum. This article fixes each of those, with worked examples in the exact style the paper rewards.

Note: this guide deliberately does not cover ray diagrams, reflection, or refraction of light — that is a separate topic. Here we focus on wave behaviour, sound, and the EM spectrum.

Describing Wave Motion: The Five Quantities You Must Define

A wave is a disturbance that transfers energy from one place to another without transferring matter. The particles of the medium vibrate about fixed positions; they do not travel along with the wave. This single sentence is worth memorising — examiners reward it.

• Amplitude (A) — the maximum displacement of a particle from its rest (equilibrium) position. Unit: metres (m). Larger amplitude means more energy carried.
• Wavelength (λ) — the distance between two consecutive points in phase, for example crest to crest or compression to compression. Unit: metres (m).
• Frequency (f) — the number of complete waves produced (or passing a point) per second. Unit: hertz (Hz), where 1 Hz = 1 wave per second.
• Period (T) — the time taken to produce one complete wave. Unit: seconds (s).
• Wave speed (v) — the distance travelled by the wave per second. Unit: metres per second (m/s).

The two key relationships

Frequency and period are reciprocals of each other:

T = 1/f and equivalently f = 1/T

The wave equation links speed, frequency, and wavelength:

v = f λ

In words: wave speed equals frequency multiplied by wavelength. From this you can also write f = v ÷ λ or λ = v ÷ f. These two equations underpin almost every calculation in this topic, so commit them to memory and practise rearranging them.

Reading wave quantities off a graph — the crucial distinction

O-Level questions show waves on two different kinds of graph, and confusing them is one of the most common mistakes:

• Displacement against distance — a snapshot of the whole wave at one instant. From this graph you read off amplitude (vertical) and wavelength (horizontal).
• Displacement against time — the motion of a single particle over time. From this graph you read off amplitude (vertical) and period (horizontal). You then use f = 1/T to get frequency.

Always check the horizontal axis label first. If it reads "distance", the horizontal repeat is the wavelength. If it reads "time", the horizontal repeat is the period.

Transverse vs Longitudinal Waves

Waves are classified by the direction the particles vibrate relative to the direction the wave travels (the direction of energy transfer).

Transverse waves

Particles vibrate at right angles (perpendicular) to the direction of energy transfer. These waves have crests (highest points) and troughs (lowest points). Examples: water waves, waves on a rope or string, and all electromagnetic waves (light, radio, etc.).

Longitudinal waves

Particles vibrate parallel to the direction of energy transfer — that is, back and forth along the same line the wave travels. These waves have compressions (regions where particles are pushed close together) and rarefactions (regions where particles are spread apart). The key example is sound.

For a longitudinal wave, one wavelength is the distance from the centre of one compression to the centre of the next compression (or rarefaction to rarefaction).

Sound as a Longitudinal Wave

Sound is produced by a vibrating source — a loudspeaker cone, a guitar string, your vocal cords. The vibration pushes and pulls on the surrounding particles, creating a travelling pattern of compressions and rarefactions. Because the particles vibrate along the direction of travel, sound is a longitudinal wave.

Sound needs a medium

Sound requires particles to pass the vibration along, so it cannot travel through a vacuum. This is a guaranteed exam point: in outer space (a vacuum) there is no sound, no matter how loud the event. Sound travels through solids, liquids, and gases — but not through empty space.

Speed of sound in different media

Sound travels fastest in solids, slower in liquids, and slowest in gases. This is because particles are closest together in solids, so the vibration is passed on most quickly. As a rough guide, the speed of sound in air is about 330–340 m/s; in water it is around 1500 m/s; in steel it is several thousand m/s. The speed of sound in air also increases slightly with temperature.

Echoes

An echo is sound reflected off a hard surface, such as a wall or cliff, and heard again after a short delay. Echoes are the basis of one of the standard methods for measuring the speed of sound.

Pitch and loudness

Two everyday properties of sound map directly onto two wave quantities:

• Pitch depends on frequency. Higher frequency means higher pitch; lower frequency means lower pitch.
• Loudness depends on amplitude. Larger amplitude means a louder sound; smaller amplitude means a softer sound.

A common confusion is to link loudness to frequency. It does not — loudness is about amplitude. Pitch is the one tied to frequency.

Ultrasound and its uses

Sound with a frequency above the upper limit of human hearing (about 20 000 Hz, i.e. 20 kHz) is called ultrasound. Its uses include:

• Medical scanning — for example, prenatal scans to image a foetus safely, because ultrasound does not use harmful ionising radiation.
• Measuring depth and distance — sonar on ships sends ultrasound pulses to the seabed and times the reflected pulse to find the depth of water.
• Detecting flaws — checking inside metal castings or pipes for cracks without cutting them open (non-destructive testing).
• Cleaning — ultrasonic baths dislodge dirt from delicate objects such as jewellery.

The Electromagnetic (EM) Spectrum

The electromagnetic spectrum is the family of transverse waves that all share three properties:

• They are all transverse waves.
• They all travel at the same speed in a vacuum — the speed of light, 3 × 10⁸ m/s.
• They can all travel through a vacuum (unlike sound), which is why light and radio reach us from space.

They differ in frequency and wavelength. In order of increasing frequency (and therefore decreasing wavelength), the seven bands are:

1. Radio waves — longest wavelength, lowest frequency.
2. Microwaves
3. Infrared
4. Visible light
5. Ultraviolet
6. X-rays
7. Gamma rays — shortest wavelength, highest frequency.

A memory aid for the order from radio to gamma is the first letters: Radio, Microwave, Infrared, Visible, Ultraviolet, X-ray, Gamma. Many students use a sentence such as "Real Marbles In Vases Use eXtra Glue". Note that the visible part itself runs from red (longest wavelength) to violet (shortest wavelength).

Uses and dangers of each band

• Radio waves — uses: broadcasting radio and television signals, and communication. Generally considered safe at normal levels.
• Microwaves — uses: microwave ovens (heating food) and mobile-phone and satellite communication. Danger: internal heating of body tissue with strong exposure.
• Infrared — uses: remote controls, thermal imaging, and short-range data links. Danger: skin burns from excessive heat.
• Visible light — uses: vision, photography, and optical-fibre communication. The only band the human eye detects.
• Ultraviolet (UV) — uses: sterilising equipment, detecting forged notes, and producing vitamin D in skin. Danger: skin cancer and eye damage; UV is ionising.
• X-rays — uses: medical imaging of bones and security scanning at airports. Danger: damages or kills living cells; ionising and can cause cancer with overexposure.
• Gamma rays — uses: sterilising medical equipment and food, and treating cancer (radiotherapy). Danger: highly ionising; severe cell damage and cancer risk.

Notice the trend: as you move towards the high-frequency end (UV, X-rays, gamma rays), the waves carry more energy and become more harmful because they are ionising.

Worked Examples

Example 1 — Using v = f λ

A water wave has a frequency of 5 Hz and a wavelength of 0.4 m. Calculate (a) its speed and (b) its period.

(a) Use v = f λ. v = 5 × 0.4 = 2 m/s

(b) Use T = 1/f. T = 1 ÷ 5 = 0.2 s

Example 2 — Finding frequency for a sound wave

A sound wave travels through air at 340 m/s. Its wavelength is 0.85 m. Calculate its frequency, and state whether a human could hear it.

Rearrange v = f λ to give f = v ÷ λ. f = 340 ÷ 0.85 = 400 Hz

Since 400 Hz lies between about 20 Hz and 20 000 Hz, this sound is within the normal range of human hearing, so yes, a human could hear it.

Example 3 — Echo method for the speed of sound

A student stands 165 m from a large wall and claps once. She hears the echo 1.0 s later. Calculate the speed of sound in air.

The sound travels to the wall and back, so the total distance is twice the distance to the wall: Total distance = 2 × 165 = 330 m

Speed = total distance ÷ time = 330 ÷ 1.0 = 330 m/s

The trap here is forgetting to double the distance. The sound makes a round trip, so you must use 2 × 165 m, not 165 m. This "there and back" idea is the same one used in sonar and ultrasound depth measurement.

Example 4 — Reading a displacement-time graph

A displacement-time graph for a single particle shows that one complete cycle takes 0.02 s and the maximum displacement is 3 mm. State the amplitude, period, and frequency.

• Amplitude = maximum displacement = 3 mm
• Period = time for one cycle = 0.02 s
• Frequency = 1 ÷ T = 1 ÷ 0.02 = 50 Hz

Because the horizontal axis is time, the repeat distance gives the period — not the wavelength. You cannot find wavelength from this graph alone.

Common Exam Traps to Avoid

Trap 1: Confusing frequency with wave speed

Frequency (Hz) is how many waves pass per second; speed (m/s) is how far the wave travels per second. Changing the frequency of a wave in a fixed medium does not change its speed — instead the wavelength adjusts, because v = f λ. For EM waves in a vacuum, the speed is always 3 × 10⁸ m/s regardless of frequency.

Trap 2: Saying sound can travel through a vacuum

Sound needs a medium of particles. In a vacuum (such as outer space) there is no sound. EM waves, by contrast, travel happily through a vacuum.

Trap 3: Mixing up amplitude and wavelength on a graph

Amplitude is always the vertical measurement (maximum displacement). Wavelength or period is the horizontal repeat. Then check whether the horizontal axis is distance (gives wavelength) or time (gives period).

Trap 4: Forgetting to double the distance in echo and sonar questions

The sound travels to the reflecting surface and back. Always use twice the one-way distance for the total path.

Trap 5: Getting the EM spectrum order wrong

From radio to gamma the order is radio, microwave, infrared, visible, ultraviolet, X-ray, gamma — increasing frequency and decreasing wavelength. Do not place X-rays before ultraviolet, and remember all seven travel at the same speed in a vacuum.

Trap 6: Linking loudness to frequency

Loudness depends on amplitude; pitch depends on frequency. Keep these two pairings separate.

Trap 7: Unit slips

Convert before substituting. Wavelengths given in cm or mm must become metres, and times in milliseconds must become seconds, before you use v = f λ or T = 1/f.

How to Practise and Revise This Topic

1. Memorise the definitions word-perfectly. Amplitude, wavelength, frequency, period, and wave speed each carry definition marks. Write them from memory until they are automatic.
2. Drill the two formulae. Practise rearranging v = f λ and T = 1/f to make any quantity the subject, and always show the rearranged equation before substituting numbers.
3. Label graphs out loud. For every wave graph, say whether the x-axis is distance or time, then mark amplitude vertically and wavelength or period horizontally.
4. Build a one-page EM spectrum table. Seven rows: band, one use, one danger. Recite it in order, radio to gamma, until you never hesitate.
5. Watch the units. Before substituting, convert everything to metres, seconds, and hertz. Many marks are lost purely to unit slips.
6. Work past-year structured questions. Aim for several O-Level Pure Physics questions that combine a wave calculation, a sound or echo problem, and an EM spectrum recall part — the way the real paper does.

Secure the definitions, the two formulae, and the EM spectrum order, and waves, sound, and the electromagnetic spectrum becomes one of the most dependable mark-earning topics in your O-Level Pure Physics paper.