General properties of waves Revision Notes

A wave is a repeating disturbance or vibration that travels through space or a medium, transferring energy from one point to another. Crucially, while energy moves with the wave, the particles of the medium do not travel along with it; instead, they oscillate around fixed positions. This means that matter itself is not transported over long distances by the wave.

For example, when you drop a pebble into a still pond, circular ripples spread outwards. The water molecules move up and down or slightly back and forth but do not travel with the ripples across the pond. The energy from the pebble’s impact moves outward, but the water remains largely in place.

• Waves transfer energy through oscillations or vibrations.
• Particles of the medium oscillate but do not travel with the wave.
• Energy moves from the source to distant points without matter displacement.

Mechanical waves require a medium such as air, water, or a solid to propagate. The energy is passed between particles of the medium through their vibrations. These vibrations cause neighbouring particles to oscillate, passing energy along the wave path.

For instance, sound waves are longitudinal mechanical waves where air particles vibrate parallel to the wave’s direction. Although the sound energy travels from a speaker to your ear, the air molecules themselves only oscillate around their equilibrium positions and do not move from the speaker to your ear.

This oscillatory motion ensures that energy is transmitted efficiently without the bulk movement of matter.

• Mechanical waves need a medium to travel.
• Energy is transferred via particle vibrations in the medium.
• Particles oscillate about fixed points, not moving with the wave.

Electromagnetic waves, such as light, radio waves, and X-rays, differ from mechanical waves because they do not require a medium to travel. They can propagate through a vacuum, such as space.

These waves consist of oscillating electric and magnetic fields that carry energy through space. Since there is no medium, no matter is involved in the transfer; energy moves through the wave itself.

For example, sunlight travels through the vacuum of space to Earth, transferring energy that warms the planet and enables photosynthesis, without any matter moving from the Sun to Earth.

• Electromagnetic waves do not require a medium.
• Energy is carried by oscillating electric and magnetic fields.
• Energy transfer occurs even through empty space.

It is important to understand the difference between energy transfer and matter movement. In wave motion, energy moves forward, but the particles of the medium only vibrate locally and do not travel with the wave.

If matter were transported with the wave, it would imply a net movement of particles from the source to the receiver, which does not happen in wave propagation.

This distinction explains why waves can transmit energy over long distances without the physical displacement of the medium’s particles.

• Energy moves forward with the wave.
• Particles oscillate but return to their original positions.
• No net transport of matter occurs in wave propagation.

A ripple tank can be used to observe wave energy transfer. When a paddle vibrates up and down in the water, waves spread out across the tank’s surface.

The water particles move in small circles or oscillations, but the water itself does not flow across the tank. Instead, the energy from the paddle’s motion travels outward as waves.

This practical illustrates how energy moves through the medium without the bulk movement of water, reinforcing the concept that waves carry energy but not matter.

• Ripple tank shows wave propagation visually.
• Water particles oscillate locally, not moving with the wave.
• Energy from the paddle is transferred across the tank.

Wave motion is the process by which energy travels through a medium by means of vibrations or oscillations. Importantly, the medium itself does not move permanently from one place to another; instead, particles of the medium oscillate around fixed positions, passing energy to neighbouring particles. This distinguishes wave motion from the movement of matter.

For example, when you shake one end of a rope, the disturbance travels along the rope as a wave, but the rope itself does not shift permanently in the direction of the wave. This principle applies to all mechanical waves, which require a medium to propagate.

• Energy transfer occurs without permanent displacement of the medium.
• Particles oscillate about fixed points, passing energy along.

Consider a rope fixed at one end. When you move the free end up and down rapidly, you create vibrations that travel along the rope as transverse waves. Each segment of the rope moves perpendicular to the direction of wave travel, oscillating up and down while the wave energy moves horizontally along the rope.

This example shows how a mechanical wave can propagate through a solid medium by successive vibrations of particles. The speed of the wave depends on the tension and mass per unit length of the rope, but the rope itself does not move along the length.

• Vibrations in the rope produce transverse waves.
• Particles move perpendicular to wave direction.
• Energy travels along the rope without the rope moving forward.

A spring or slinky demonstrates wave motion through longitudinal waves. When one end of the spring is compressed and released, a compression wave travels along the coils. The coils oscillate back and forth parallel to the direction of wave travel, transmitting energy through the spring.

This shows how energy can be transferred by compressions and rarefactions in a medium. The coils themselves do not move along the spring; instead, they vibrate around their equilibrium positions, passing the disturbance along.

• Longitudinal waves involve vibrations parallel to wave travel.
• Compression and extension of coils transmit energy.
• The spring’s coils oscillate without permanent displacement.

Water waves on the surface of a pond or tank provide a clear visual example of wave motion. When a disturbance, such as a pebble dropped into water, creates ripples, energy moves outward across the surface.

Water particles move in circular or elliptical orbits, oscillating up and down and slightly forward and backward, but they do not travel with the wave. Instead, the wave pattern moves across the surface, carrying energy away from the source.

This oscillatory motion of particles in water waves is a combination of transverse and longitudinal components, illustrating complex wave behaviour in fluids.

• Water particles oscillate in circular paths.
• Energy moves across the surface as waves.
• Particles return to their original positions after oscillation.

A simple experiment to observe wave motion involves creating waves in a shallow water tank. By gently disturbing the water surface with a finger or a small object, ripples form and travel outward.

Measuring the distance between wave crests (wavelength) and timing how long waves take to travel a known distance allows calculation of wave speed using the formula v = f × λ, where f is frequency and λ is wavelength.

Repeating measurements improves accuracy. Observations confirm that water particles oscillate locally while the wave energy moves across the surface, demonstrating wave motion principles practically.

• Create ripples by disturbing water surface.
• Measure wavelength and frequency to find wave speed.
• Observe particle oscillation versus wave propagation.
• Repeat for reliable data and confirm energy transfer without particle displacement.

Waves are disturbances that transfer energy through a medium or space without the permanent displacement of matter. To understand how waves behave and carry energy, it is essential to identify their key characteristics. These include wavelength, frequency, crest, trough, amplitude, and wave speed. Each property provides specific information about the wave's structure and dynamics.

Wavelength (λ) is the distance between two successive points on a wave that are in phase, commonly measured between two crests or two troughs. It is expressed in metres (m). For example, if the distance between two crests on a water wave is 0.5 m, then the wavelength is 0.5 m.

Frequency (f) is the number of complete waves passing a fixed point per second, measured in hertz (Hz). A frequency of 2 Hz means two waves pass the point every second. Frequency is determined by the source of the wave, such as a vibrating string or a speaker cone.

Wavelength and frequency are inversely related for waves travelling at a constant speed: as frequency increases, wavelength decreases, and vice versa.

• Wavelength (λ): distance between two crests or troughs, in metres (m).
• Frequency (f): number of waves passing a point per second, in hertz (Hz).

The crest of a wave is the highest point above the rest (equilibrium) position, while the trough is the lowest point below it. These points represent the maximum positive and negative displacements of the wave.

Amplitude (A) is the maximum displacement of a point on the wave from its rest position. It is measured in metres (m) and relates directly to the energy carried by the wave: larger amplitudes mean more energy. For example, a loud sound wave has a greater amplitude than a quiet one.

Amplitude differs from wavelength; amplitude measures vertical displacement, while wavelength measures horizontal distance between repeating points.

• Crest: highest point of the wave.
• Trough: lowest point of the wave.
• Amplitude (A): maximum displacement from rest position, indicating wave energy.

Wave speed (v) is the distance a wave travels per unit time, measured in metres per second (m/s). It depends on the medium through which the wave travels and the type of wave.

Wave speed is calculated using the formula: v = f × λ, where f is frequency in hertz and λ is wavelength in metres.

For example, if a wave has a frequency of 5 Hz and a wavelength of 0.2 m, then its speed is v = 5 Hz × 0.2 m = 1 m/s. This means the wave moves 1 metre every second.

• Wave speed (v) = frequency (f) × wavelength (λ).
• Units: speed in m/s, frequency in Hz, wavelength in m.

Consider water waves generated by dropping a stone into a pond. The distance between two wave crests on the water surface is measured as 0.4 m (wavelength). Counting the number of crests passing a fixed point in 10 seconds gives 20 waves, so frequency is 20 ÷ 10 = 2 Hz.

Using the formula v = f × λ, wave speed is 2 Hz × 0.4 m = 0.8 m/s. This means the wave fronts travel across the pond at 0.8 metres per second.

Observing the height of the crests above the calm water level gives the amplitude, which relates to the energy transferred by the waves.

• Measure wavelength between crests: 0.4 m.
• Count waves passing a point in time to find frequency: 2 Hz.
• Calculate wave speed: 0.8 m/s.

When a wave encounters a flat, smooth surface, it bounces back into the original medium. This process is called reflection. The wave does not pass through or get absorbed significantly but reverses direction.

The key principle governing reflection is that the angle at which the wave arrives at the surface, called the angle of incidence, is exactly equal to the angle at which it reflects away, called the angle of reflection. Both angles are measured relative to an imaginary line perpendicular to the surface, known as the normal.

For example, if a water wave approaches a straight wall at 30°, it will reflect off the wall at 30° on the opposite side of the normal. This predictable behaviour allows us to trace wave paths and understand phenomena such as echoes in sound waves or light reflections in mirrors.

• Reflection occurs when waves bounce off a surface.
• Angle of incidence = Angle of reflection.
• Angles are measured relative to the normal (perpendicular) to the surface.

Refraction happens when a wave passes from one medium into another where its speed is different. Because the wave speed changes, the wave changes direction, bending towards or away from the normal line.

This bending occurs because one side of the wavefront enters the new medium before the other side, causing the wave to pivot. The amount of bending depends on the ratio of the wave speeds in the two media and the angle at which the wave enters the new medium.

For example, when light travels from air into water, it slows down. If it hits the water surface at an angle, it bends towards the normal. Conversely, when it moves from water back into air, it speeds up and bends away from the normal.

• Refraction is the bending of waves due to speed change between media.
• Wave speed decreases or increases depending on the medium.
• The wave bends towards the normal if it slows down, away if it speeds up.

The wave speed (v), frequency (f), and wavelength (λ) are related by the formula v = f × λ. When a wave enters a new medium and its speed changes, its frequency remains constant because the source frequency does not change.

Since frequency is constant, a change in speed results in a change in wavelength. This change in wavelength is what causes the wave to bend during refraction.

For example, if a wave slows down on entering a denser medium, its wavelength shortens, causing the wavefront to change direction.

• Wave speed formula: v = f × λ
• Frequency remains constant during refraction.
• Change in speed causes change in wavelength and direction.

Reflection is observed in everyday life, such as light reflecting off mirrors or sound waves producing echoes from walls. Water waves reflecting off barriers also demonstrate this effect.

Refraction is seen when a straw in a glass of water appears bent at the water surface or when light passes through lenses to focus images. These examples illustrate how wave speed changes cause bending of waves.

Understanding these effects is essential in designing optical devices, sonar, and understanding natural phenomena.

• Light reflecting in mirrors and sound echoes show reflection.
• Straw appearing bent in water demonstrates refraction.
• Lenses use refraction to focus light.

Reflection involves waves bouncing off surfaces with equal angles of incidence and reflection.

Refraction occurs when waves change speed entering a new medium, causing them to bend.

Wave frequency remains constant during refraction, so changes in speed affect wavelength and direction of the wavefront.

• Reflection: angle of incidence = angle of reflection.
• Refraction: wave bends due to speed change between media.
• Frequency constant; wavelength and direction change during refraction.

A wave transfers energy through a medium or space without transporting matter. The speed of a wave (v) is the distance the wave travels per unit time. Two key properties determine wave speed: frequency (f) and wavelength (λ). Frequency is how many wave cycles pass a point each second, measured in hertz (Hz). Wavelength is the distance between two consecutive points in phase on the wave, such as crest to crest, measured in metres (m).

• Wave speed (v) is the rate of wave travel in metres per second (m/s).
• Frequency (f) is the number of waves passing a point per second, in hertz (Hz).
• Wavelength (λ) is the length of one complete wave cycle, in metres (m).

The formula v = f λ links wave speed, frequency, and wavelength. It states that wave speed equals frequency multiplied by wavelength. This means if either frequency or wavelength increases while the other remains constant, the wave speed changes accordingly.

This formula applies to all types of waves, including sound waves, water waves, and electromagnetic waves, provided the medium and conditions are consistent.

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

To calculate wave speed, first identify the frequency and wavelength values with their units. Then multiply frequency by wavelength to find speed. Always include units in your calculation to ensure the answer is physically meaningful.

For example, if a wave has a frequency of 5 Hz and a wavelength of 2 m, the wave speed is:

v = f × λ = 5 Hz × 2 m = 10 m/s. This means the wave travels 10 metres every second.

• Identify frequency (f) and wavelength (λ) with correct units.
• Multiply f by λ to find wave speed (v).
• Include units in the final answer (m/s).

Sometimes you may need to find frequency or wavelength instead of wave speed. Rearranging the formula helps:

Frequency: f = v / λ (wave speed divided by wavelength)

Wavelength: λ = v / f (wave speed divided by frequency)

• Use f = v / λ to find frequency if wave speed and wavelength are known.
• Use λ = v / f to find wavelength if wave speed and frequency are known.
• Always check units to keep consistency.

After calculation, verify that the units of your answer are correct and that the value is reasonable. For example, wave speeds in air are typically around 340 m/s for sound, so a calculated speed of 10,000 m/s would be unrealistic for sound waves in air.

If units do not match or the value is unreasonable, re-examine your substitutions and unit conversions.

• Confirm final units are metres per second (m/s) for wave speed.
• Compare calculated values to typical wave speeds for the wave type.
• Review calculations if results seem inconsistent.

A transverse wave is a type of wave in which the particles of the medium vibrate at right angles (perpendicular) to the direction the wave travels. This means if the wave moves horizontally, the particles move vertically or side to side. This contrasts with longitudinal waves, where vibrations are parallel to wave travel.

The perpendicular vibration causes characteristic wave features such as crests (high points) and troughs (low points). These features are visible in many transverse waves and help distinguish them from other wave types.

• Vibration direction ⟂ wave travel direction
• Particles move up/down or side/side while wave moves forward
• Crests and troughs are typical features

Electromagnetic waves, including visible light, radio waves, and X-rays, are transverse waves. They consist of oscillating electric and magnetic fields perpendicular to each other and to the direction of wave travel.

Because electromagnetic waves do not require a medium, their transverse nature allows them to propagate through a vacuum, such as space. The perpendicular vibrations of the fields enable energy transfer without particle displacement in a medium.

• Electric and magnetic fields oscillate perpendicular to wave direction
• Can travel through vacuum (no medium needed)
• Examples: visible light, radio waves, X-rays

Water waves on the surface of a pond or sea are transverse waves where water particles move in roughly circular paths. At the surface, particles move up and down (perpendicular to wave travel) and slightly forward and backward, but the dominant motion is vertical.

This vertical vibration creates the visible crests and troughs of waves. Although water waves have some longitudinal components, the transverse motion is the defining characteristic for this objective.

• Water particles move mainly up/down at surface
• Creates visible crests and troughs
• Example: waves on a pond or ocean

Seismic S-waves (secondary waves) are transverse waves that travel through the Earth during an earthquake. The particles in rocks vibrate perpendicular to the wave's direction, causing shaking at right angles to the wave travel path.

S-waves cannot travel through liquids, which helps seismologists understand Earth's internal structure. Their transverse nature causes more destructive shaking compared to longitudinal P-waves.

• Particles vibrate perpendicular to wave travel
• Cannot pass through liquids
• Cause side-to-side shaking during earthquakes

Knowing that transverse waves vibrate perpendicular to their travel direction helps predict wave behaviour, interactions with materials, and energy transfer.

For example, polarisation is a property unique to transverse waves, where vibrations can be filtered in certain directions. This property is used in sunglasses and photography.

Recognising examples of transverse waves aids in identifying wave types in different contexts, essential for problem-solving in physics.

• Determines wave properties like polarisation
• Affects how waves interact with materials
• Helps classify and understand wave types

Longitudinal waves are mechanical waves where the particles of the medium vibrate parallel to the direction in which the wave travels. This means that as the wave moves forward, particles oscillate back and forth along the same line as the wave propagation.

Unlike transverse waves, where vibrations are perpendicular to wave travel, longitudinal waves involve compressions and rarefactions—regions where particles are pushed together or spread apart, respectively. These alternating compressions and rarefactions move through the medium, transferring energy from one location to another without the particles themselves travelling the full distance.

• Particle vibration direction is parallel to wave travel.
• Wave consists of compressions (high pressure) and rarefactions (low pressure).
• Energy transfer occurs through particle oscillations, not particle displacement.

Sound waves in air are classic examples of longitudinal waves. When a sound is produced, such as a vibrating guitar string, it causes nearby air particles to oscillate along the direction the sound wave travels.

These oscillations create alternating compressions and rarefactions in the air, which propagate outward from the source. The speed of sound in air at room temperature is approximately 343 m/s, but this depends on factors like temperature and medium.

Because the particles only vibrate around their equilibrium positions, the air itself does not move from the source to the listener; instead, the energy of the sound wave travels through the medium.

• Sound waves involve air particle vibrations parallel to wave direction.
• Compressions and rarefactions transmit sound energy.
• Speed of sound in air is about 343 m/s at 20°C.

Seismic P-waves, or primary waves, are longitudinal waves generated by earthquakes. They travel through the Earth’s interior by compressing and expanding the rock particles in the direction of wave travel.

P-waves are the fastest seismic waves and arrive first at seismic detectors. Their longitudinal nature allows them to travel through solids, liquids, and gases, unlike some other seismic waves.

The particle motion in P-waves is similar to sound waves but occurs in solid rock, causing alternating compressions and expansions that transmit energy through the Earth.

• P-waves vibrate particles parallel to wave travel direction.
• They can move through solids, liquids, and gases.
• They are the fastest seismic waves and first detected after an earthquake.

In longitudinal waves, although particles vibrate back and forth, they do not travel with the wave. Instead, energy is passed along by these oscillations.

For example, in sound waves, air particles oscillate around fixed positions, transmitting sound energy without the air itself moving from source to listener.

This principle is crucial for understanding wave behaviour: waves transfer energy through a medium without transporting matter over long distances.

• Particles oscillate around fixed points, not moving permanently.
• Energy is transferred through particle vibrations.
• This distinguishes wave energy transfer from bulk matter movement.