P5: Waves in Matter

What you'll learn

This revision guide covers all testable content on waves in matter from the OCR GCSE Physics specification. You'll explore how mechanical waves transfer energy through substances, the differences between longitudinal and transverse waves, and how to calculate wave properties. This topic is fundamental to understanding sound, seismic waves, and wave behaviour in everyday contexts.

Key terms and definitions

Mechanical wave — A wave that requires a medium (solid, liquid or gas) to travel through and cannot propagate in a vacuum

Longitudinal wave — A wave where particle oscillations are parallel to the direction of energy transfer, creating compressions and rarefactions

Transverse wave — A wave where particle oscillations are perpendicular to the direction of energy transfer, creating peaks and troughs

Amplitude — The maximum displacement of a particle from its rest position, measured in metres (m)

Wavelength (λ) — The distance between two adjacent points in phase on a wave, such as crest to crest or compression to compression, measured in metres (m)

Frequency (f) — The number of complete wave cycles passing a point per second, measured in hertz (Hz)

Wave speed (v) — The distance travelled by a wave per unit time, measured in metres per second (m/s)

Period (T) — The time taken for one complete wave cycle, measured in seconds (s)

Core concepts

Types of mechanical waves

Mechanical waves require a medium to propagate. Unlike electromagnetic waves, they cannot travel through a vacuum because they rely on particle interactions to transfer energy.

Transverse waves:

• Particles oscillate at right angles to wave direction
• Create peaks (crests) and troughs
• Examples include waves on water surfaces, waves on strings, and seismic S-waves
• Can be demonstrated using a slinky moved side-to-side or a rope flicked up and down

Longitudinal waves:

• Particles oscillate parallel to wave direction
• Create compressions (regions where particles are close together) and rarefactions (regions where particles are spread apart)
• Examples include sound waves in air, ultrasound in tissues, and seismic P-waves
• Can be demonstrated using a slinky pushed and pulled along its length

Both wave types transfer energy without permanently transferring matter. Individual particles vibrate about fixed positions but return to their original location after the wave passes.

Wave properties and measurements

Understanding how to identify and measure wave properties is essential for calculations and practical work.

Amplitude determines the energy carried by a wave. Larger amplitude means:

• Greater energy transfer
• Louder sounds (for sound waves)
• Larger water wave height

Wavelength can be measured:

• Peak to peak or trough to trough for transverse waves
• Compression to compression or rarefaction to rarefaction for longitudinal waves
• Using rulers or metre sticks in practical investigations

Frequency relates to:

• Pitch in sound waves (higher frequency = higher pitch)
• Period by the equation: f = 1/T
• Number of waves per second passing a fixed point

Period represents the time for one complete oscillation and connects to frequency through the reciprocal relationship.

The wave equation

The wave equation connects speed, frequency and wavelength:

v = f × λ

Where:

• v = wave speed (m/s)
• f = frequency (Hz)
• λ = wavelength (m)

This equation applies to all waves, including mechanical and electromagnetic waves. You must be able to:

• Rearrange the equation to find any variable
• Convert units appropriately (e.g., kHz to Hz, cm to m)
• Use standard form for very large or small values

Rearrangements:

• f = v/λ
• λ = v/f

Remember that wave speed depends on the medium, not the frequency. In a given medium, if frequency increases, wavelength must decrease proportionally to keep wave speed constant.

Sound waves

Sound is a longitudinal wave that travels through solids, liquids and gases but not through a vacuum.

Speed of sound in different media:

• Air (20°C): approximately 330 m/s
• Water: approximately 1500 m/s
• Steel: approximately 5000 m/s

The speed increases with:

• Density of the medium (generally)
• Temperature (in gases)
• Stronger particle interactions

Human hearing range:

• Audible frequencies: approximately 20 Hz to 20,000 Hz (20 kHz)
• Ultrasound: frequencies above 20 kHz (beyond human hearing)
• Infrasound: frequencies below 20 Hz (below human hearing)

Applications of ultrasound:

• Medical imaging (pregnancy scans, kidney stones)
• Industrial flaw detection in materials
• Distance measurement (sonar, depth finding)
• Cleaning delicate instruments

Ultrasound is useful because:

• It reflects at boundaries between different media
• High frequencies provide detailed images
• It's non-ionising and therefore safer than X-rays for soft tissue

Reflection of sound waves

Sound waves obey the law of reflection: angle of incidence equals angle of reflection, measured from the normal.

Echo — A reflected sound wave that arrives with sufficient time delay to be distinguished from the original sound

Echoes occur when sound reflects from hard, smooth surfaces like walls, cliffs or canyon walls. Soft, porous materials absorb sound rather than reflecting it, which is why recording studios use acoustic foam.

Using echoes to measure distance:

If you measure the time delay between making a sound and hearing the echo, you can calculate distance using:

distance = (speed × time) ÷ 2

The division by 2 accounts for the sound travelling to the reflector and back.

Seismic waves

Earthquakes produce two types of seismic waves that travel through Earth:

P-waves (Primary waves):

• Longitudinal waves
• Travel through solids, liquids and gases
• Faster than S-waves (arrive first at seismometer stations)
• Cause less damage

S-waves (Secondary waves):

• Transverse waves
• Only travel through solids
• Slower than P-waves
• Cause more ground shaking and damage

The fact that S-waves cannot pass through Earth's outer core (they disappear and create a "shadow zone") provides evidence that the outer core is liquid. P-waves can travel through it but are refracted, creating their own shadow zone.

Seismologists use arrival times at different monitoring stations to:

• Locate earthquake epicentres through triangulation
• Study Earth's internal structure
• Estimate earthquake magnitude and energy

Wave interactions in matter

When waves travel through matter, several phenomena occur:

Absorption — Wave energy is transferred to the medium, often converting to heat. This reduces amplitude and intensity as the wave propagates.

Transmission — Waves pass through a substance. The amount transmitted depends on the medium's properties and wave frequency.

Reflection — Waves bounce off boundaries between different media. Hard, dense boundaries reflect more energy than soft, porous ones.

The proportion of energy reflected, transmitted or absorbed depends on:

• The nature of the boundary
• The wavelength/frequency of the wave
• The materials' acoustic properties

In medical ultrasound, different tissue types reflect different amounts of sound energy, creating the contrast in images.

Worked examples

Example 1: Wave speed calculation

Question: A sound wave in air has a frequency of 440 Hz and a wavelength of 0.75 m. Calculate the speed of the sound wave. [3 marks]

Solution:

• Write the wave equation: v = f × λ [1 mark]
• Substitute values: v = 440 × 0.75 [1 mark]
• Calculate and state units: v = 330 m/s [1 mark]

Examiner tip: Always show your working clearly. Even if the final answer is wrong, you can gain marks for correct method and equation.

Example 2: Calculating distance using echoes

Question: A boat uses sonar to detect the seabed. The ultrasound pulse reflects off the seabed and returns to the boat 0.40 s after being emitted. The speed of sound in seawater is 1500 m/s. Calculate the depth of water beneath the boat. [4 marks]

Solution:

• Calculate total distance travelled: distance = speed × time = 1500 × 0.40 = 600 m [1 mark]
• Recognise sound travels down and back (twice the depth) [1 mark]
• Divide by 2: depth = 600 ÷ 2 [1 mark]
• State answer with unit: depth = 300 m [1 mark]

Examiner tip: The "divide by 2" step is crucial in echo/reflection questions. Many students forget this.

Example 3: Frequency and period relationship

Question: A wave on a string has a period of 0.05 s. (a) Calculate the frequency of the wave. [2 marks] (b) If the wavelength is 2.5 m, calculate the wave speed. [2 marks]

Solution: (a)

• Use equation: f = 1/T [1 mark]
• Calculate: f = 1/0.05 = 20 Hz [1 mark]

(b)

• Use equation: v = f × λ = 20 × 2.5 [1 mark]
• Calculate: v = 50 m/s [1 mark]

Common mistakes and how to avoid them

• Forgetting to halve the distance in echo calculations — Remember sound travels to the reflector AND back, so you must divide the total distance by 2 to find the actual distance to the object

• Confusing wave speed with particle speed — Wave speed is how fast the wave pattern moves; particles only vibrate about fixed positions. The medium doesn't travel with the wave

• Mixing up transverse and longitudinal — Remember: transverse = perpendicular oscillations (like waves on water); longitudinal = parallel oscillations (like sound). Don't just memorise examples; understand the particle motion

• Unit conversion errors — Always convert to standard units before calculating: kHz → Hz (×1000), cm → m (÷100). Write conversions clearly in your working

• Stating that sound cannot travel through solids or liquids — Sound is a mechanical wave that travels through all states of matter (often faster in solids), just not through a vacuum

• Reversing the frequency-period relationship — Remember f = 1/T, not T = 1/f (though both are mathematically equivalent). Check your answer makes sense: high frequency means short period

Exam technique for "P5: Waves in Matter"

• Command word awareness: "Calculate" requires numerical working with units; "Describe" needs clear statements about what happens; "Explain" requires reasons using physics principles. For 3-mark calculations, expect: equation, substitution, answer with unit

• Drawing wave diagrams: Use a ruler for straight parts, clearly label amplitude and wavelength with arrows, and mark at least two complete wave cycles. For longitudinal waves, show compressions as dense particle regions and rarefactions as sparse regions

• Extended response questions: Structure answers using connectives (because, therefore, this causes). For 6-mark questions on wave applications, discuss the physics principle first, then the specific application, then any limitations or benefits

• Practical questions: If asked about measuring wave speed in a ripple tank or on a string, mention measuring multiple wavelengths then dividing (reduces percentage error), using a strobe or slow-motion camera for fast waves, and repeating measurements for reliability

Quick revision summary

Mechanical waves require a medium to travel. Transverse waves oscillate perpendicular to energy transfer; longitudinal waves oscillate parallel to it. Use v = f × λ to calculate wave properties in any medium. Sound travels as longitudinal waves at different speeds through different materials, with ultrasound (>20 kHz) used in medical and industrial applications. Echo timing allows distance measurement: remember to halve the total distance. Seismic P-waves (longitudinal) and S-waves (transverse) reveal Earth's structure because S-waves cannot pass through liquids.