0625 · 3.1General properties of waves

Wave energy and key properties

0:00A flick of your hand sends a bump along a rope. The bump travels away, but the rope does not travel with it. A ribbon tied to the rope moves up and down as the disturbance passes. That difference between the travelling disturbance and the moving material is the starting point for understanding waves. By the end of this video, you will understand how waves carry energy and how we describe their shape and motion.

0:21You will also see why waves reflect, refract and spread out. We will connect these ideas using ropes, springs and water waves, then practise calculations and an exam-style explanation. We need just two starting ideas. A vibration is a repeated movement about an equilibrium position. The equilibrium position is where something normally rests. Speed tells us how far something travels each second. With waves, we must distinguish the speed of the travelling disturbance from the movement of individual particles.

0:50Waves transfer energy without transferring matter. When you shake a rope, neighbouring sections pull on each other, passing the disturbance along. Each section moves about its own equilibrium position instead of travelling to the far end. Energy reaches distant sections even though the material does not move along with the wave. Water waves show the same distinction. A small floating cork bobs as ripples pass, rather than travelling across the water with every crest.

1:13The advancing pattern carries energy away from the source. For this topic, we model water waves as transverse, focusing on their up-and-down movement rather than the full motion of water particles. Imagine freezing a regularly vibrating rope at one instant. Its highest points are called crests, or peaks, and its lowest points are called troughs. The equilibrium line passes through the middle. This snapshot shows how different positions along the rope are displaced at the same moment, not how one point changes over time.

1:43Amplitude is the maximum displacement from the equilibrium position. On this diagram, measure it vertically from the equilibrium line to a crest or a trough. Measuring from a crest all the way to a trough gives twice the amplitude. Amplitude describes how far the material vibrates, not how far the wave travels. Wavelength is the distance between two consecutive points in phase. Points in phase are at the same stage of their vibration.

2:07Adjacent crests are one wavelength apart, as are adjacent troughs. A crest and the next trough are only half a wavelength apart, because they are at opposite stages of the pattern. Frequency is the number of complete waves passing a point per second. Equivalently, it is the number of complete vibrations made each second. Its unit is the hertz, meaning one complete cycle per second. A frequency of five hertz means five complete waves pass a fixed point every second.

2:34Wave speed is the distance travelled by a wave per unit time. Follow a particular crest to measure this, rather than following a particle vibrating up and down. A wave diagram can therefore describe two different movements. The wave travels through the material while the material vibrates about its equilibrium position. A wavefront is a line joining points on a wave that are in phase. Viewed from above, a circular water-wave crest forms a circular wavefront.

2:58Straight crests form straight wavefronts. The direction of wave travel is perpendicular to the wavefronts, so circular waves travel outwards and straight wavefronts travel straight ahead.

Wave speed calculations

3:09The wave-speed equation follows directly from the repeating pattern. During one complete vibration, the wave advances by one wavelength. If four complete waves pass each second, four wavelengths travel past each second. The distance travelled in one second is therefore the number of waves multiplied by the length of each wave. Wave speed equals frequency multiplied by wavelength. Use metres per second for speed, hertz for frequency, and metres for wavelength.

3:36The equation links the speed of the pattern to its spacing and repetition rate. Amplitude is not part of this relationship, because height does not tell us how quickly crests move forwards. For our first calculation, water waves have a frequency of five hertz and a wavelength of eight centimetres. We want their wave speed, so we use speed equals frequency multiplied by wavelength. First, convert eight centimetres to zero point zero eight metres.

3:59This ensures the answer will be in metres per second. Next, multiply five by zero point zero eight. The wave speed is zero point four metres per second. This means a crest travels forty centimetres in one second. Five wavelengths pass during that second, and each is eight centimetres long, so the calculation agrees with the physical picture. For our second calculation, a rope wave travels at three metres per second with a frequency of six hertz.

4:24This time, the unknown is wavelength. Rearrange the equation so wavelength equals wave speed divided by frequency. Then divide three metres per second by six hertz to obtain zero point five metres. The wavelength is therefore half a metre. This makes sense because six complete wavelengths must fit into the three metres travelled each second. Always identify the unknown before choosing your calculation. Also check whether the question gives wavelength in centimetres or millimetres, because those lengths must be converted into metres.

Transverse and longitudinal waves

4:53A transverse wave has vibrations at right angles to the direction of propagation. Propagation means the direction in which the wave travels. On our rope, the wave moves horizontally while each section vibrates vertically. The two directions are perpendicular, so the rope wave is transverse regardless of how large its amplitude is. Electromagnetic radiation, water waves and seismic secondary waves can be modelled as transverse. Seismic secondary waves are commonly called S waves and travel through the Earth after an earthquake.

5:24Electromagnetic waves do not require material particles to vibrate. Their classification still depends on vibrations being perpendicular to the direction of propagation. Now push and pull the end of a stretched spring along its length. Regions of closely packed coils travel along the spring. Between them are regions with more widely spaced coils. Individual coils move backwards and forwards along the same direction as the travelling disturbance. They do not travel along the spring with each compression.

5:50A longitudinal wave has vibrations parallel to the direction of propagation. A compression is a region where particles are closer together. A rarefaction is a region where particles are farther apart. One wavelength can be measured between the centres of adjacent compressions, or between the centres of adjacent rarefactions. Sound waves and seismic primary waves can be modelled as longitudinal. Seismic primary waves are commonly called P waves. For both wave types, compare the direction of vibration with the direction of travel.

6:19A drawing that looks wavy is not enough to identify the type, because graphs can represent longitudinal waves too.

Reflection and refraction

6:26A ripple tank makes wave behaviour visible. It contains shallow water, and a vibrating straight bar can produce straight wavefronts. A lamp above the tank projects the ripple pattern onto a screen below. We can then add barriers or change the water depth to investigate reflection, refraction and diffraction. Reflection happens when a wave reaches a surface and returns into the region it came from. In a ripple tank, place a straight barrier in the path of straight water waves.

6:51The incoming wavefronts are reflected by this plane surface. The reflected waves travel away from the barrier instead of passing through it. Draw a normal perpendicular to the reflecting surface where the wave arrives. The angle of incidence equals the angle of reflection. Both angles are measured from the normal. Measure these using the directions of travel, not the wavefronts themselves. The reflected wave remains in the same water depth, so its speed is unchanged.

7:16Refraction occurs because a wave changes speed as it enters a different region. In a ripple tank, place a glass plate under part of the water to create a shallower region. Water waves travel more slowly over that plate. Their wavefronts become closer together as they cross from deeper water into shallower water. The frequency stays the same because the vibrating source still produces the same number of waves each second.

7:37Since speed equals frequency multiplied by wavelength, a lower speed means a shorter wavelength. This explains the smaller spacing between wavefronts. The source sets their arrival rate, while the water depth affects their speed. When the waves arrive obliquely, one end of each wavefront reaches shallow water first and slows first. The other end continues faster for a little longer, so the wavefront turns. The direction of travel bends towards the normal.

8:02Entering deeper water reverses this change, so the waves speed up and bend away from the normal. A speed change does not always produce a direction change. Waves travelling straight along the normal enter the new depth across the whole wavefront at once. Their speed and wavelength change, but their direction does not. This is why an explanation of refraction should identify the speed change, rather than only mentioning bending.

Diffraction through gaps and edges

8:25Diffraction is the spreading of waves through a gap or around an edge. Place two barriers across a ripple tank, leaving a gap between them. Straight waves pass through the opening and spread into the region beyond it. This is different from refraction because no change of water depth is needed. The next comparisons are Supplement content for Extended students. Diffraction through a gap depends on the gap width compared with the wavelength.

8:48When the gap width is comparable to the wavelength, spreading is pronounced. The emerging wavefronts are strongly curved, so the wave travels in a wider range of directions. With a much wider gap, most of each wavefront continues almost straight ahead. Spreading still occurs near the edges, but it is less noticeable across the transmitted wave. For a fixed wavelength, reducing gap width increases diffraction. The important comparison is relative size, not simply whether an opening looks narrow to us.

9:15For a fixed gap width, increasing wavelength also increases diffraction. Longer waves spread more because the opening is smaller relative to their wavelength. In a ripple tank, compare different wavelengths while keeping the gap unchanged. Measure the wavefront spacing to confirm the wavelength, then compare the spreading. Diffraction also occurs around a single edge. Place a barrier partway across the ripple tank and observe waves passing its free end. Wavefronts curve into the region behind the barrier instead of leaving a completely sharp boundary.

9:45For Extended students, increasing wavelength produces greater diffraction around the same edge.

Exam explanations and recap

9:50An exam question might show water waves crossing from deep water into shallow water at an angle. It could ask you to describe and explain the changes. First identify the depth change, then connect speed, frequency and wavelength. Finally, explain the direction change using the different arrival times along each wavefront. The wave speed decreases in shallow water. The frequency remains unchanged because the source frequency is unchanged. The wavelength decreases because wave speed equals frequency multiplied by wavelength.

10:20The waves bend towards the normal because one end of each wavefront slows before the other end. Another question might ask you to draw diffraction through a wavelength-sized gap. Draw curved wavefronts spreading from the opening. Keep the spacing between successive wavefronts the same as before the gap. In unchanged water depth, speed and frequency remain unchanged, so wavelength remains unchanged too. Diffraction changes the spreading pattern, not automatically the distance between wavefronts.

10:47Keep wavelength and amplitude separate when reading a diagram. Wavelength measures the repeating distance along the wave, while amplitude measures maximum displacement from equilibrium. Frequency counts complete cycles, not individual crests and troughs as separate cycles. For transverse and longitudinal waves, always compare vibration with propagation rather than relying on the drawing’s appearance. Also keep the three behaviours distinct. Reflection sends waves back from a surface, while refraction results from a speed change.

11:16Diffraction spreads waves through gaps or around edges. During refraction, frequency remains unchanged. During diffraction in unchanged water depth, the wavelength stays the same even though the wavefronts curve. The central idea is that waves transfer energy without transferring matter. Their motion is described using amplitude, wavelength, frequency, wavefronts and wave speed. Speed equals frequency multiplied by wavelength because each complete cycle advances the pattern by one wavelength. These relationships let you explain wave diagrams rather than simply memorising their labels.

11:47Transverse vibrations are perpendicular to propagation, while longitudinal vibrations are parallel to it. Ripple tanks reveal reflection, depth-dependent refraction and diffraction through gaps or around edges. Greater wavelength produces greater diffraction for the same opening or edge. With those ideas connected, you can predict how a wave pattern will behave.