General properties of waves

A wave is a disturbance that transfers energy from one place to another without transferring matter. Think of a Mexican wave in a stadium: the 'wave' moves around the stadium, but each person just stands up and sits down. The people don't move, but the energy does. There are two main types of waves. In transverse waves, the particles oscillate (vibrate) perpendicular (at 90 degrees) to the direction the wave's energy is travelling. Examples include light, all electromagnetic waves, and ripples on water. In longitudinal waves, the particles oscillate parallel to the direction of energy transfer. Sound waves are the key example of longitudinal waves.

To understand waves, we use specific terms. The Amplitude is the maximum displacement of a particle from its undisturbed rest position. For a water wave, it's the height of a crest above the normal water level. The Wavelength (symbol λ, 'lambda') is the distance between one point on a wave and the same point on the next wave, for example, from crest to crest. The Frequency (symbolf) is the number of complete waves that pass a point per second, measured in Hertz (Hz). The Period (symbol T) is the time it takes for one complete wave to pass a point, measured in seconds (s). Frequency and period are related by the simple equation T = 1/f.

There is a crucial relationship that links the speed of a wave with its frequency and wavelength. The wave speed equation is one of the most important formulas in this topic. It states that the speed of a wave is the product of its frequency and its wavelength. The equation is: wave speed = frequency × wavelength, or in symbols, v = f × λ. For this equation to work correctly, you must use standard SI units: speed(v) in metres per second (m/s), frequency(f) in Hertz (Hz), and wavelength (λ) in metres (m).

Waves can interact with barriers and boundaries in three important ways, often demonstrated in a ripple tank.

1. Reflection: This is when a wave bounces off a surface. The angle at which the wave hits the surface (angle of incidence) is equal to the angle at which it reflects (angle of reflection).
2. Refraction: This is the change in direction of a wave as it passes from one medium to another, caused by a change in speed. For example, water waves slow down and bend as they move from deep to shallow water. When a wave slows down, its wavelength decreases, but its frequency stays the same.
3. Diffraction: This is the spreading out of waves as they pass through a gap or around an obstacle. The effect is most significant when the size of the gap is similar to the wavelength of the waves. Longer wavelengths diffract more than shorter wavelengths.

Sound is produced by vibrating objects, such as a guitar string, a loudspeaker cone, or your vocal cords. These vibrations are passed through a medium (a substance like a solid, liquid, or gas) as a longitudinal wave. As the object vibrates forwards, it pushes particles together, creating a region of high pressure called a compression. As it vibrates backwards, it leaves a region of low pressure called a rarefaction. This series of compressions and rarefactions travels outwards, carrying sound energy. Because sound relies on particle vibrations, it cannot travel through a vacuum where there are no particles. Sound travels at different speeds in different media: it is fastest in solids, slower in liquids, and slowest in gases, because the particles are closer together in solids, allowing vibrations to be passed on more quickly.

Sounds have two main characteristics: pitch and loudness. Pitch describes how high or low a sound is, and it is determined by the wave's frequency. A high frequency wave produces a high-pitched sound, while a low frequency wave produces a low-pitched sound. Loudness is determined by the wave's amplitude. A wave with a large amplitude carries more energy and sounds louder. A wave with a small amplitude is quieter. We can visualise sound waves using a Cathode-Ray Oscilloscope (CRO). The CRO displays a graph of the wave, with the vertical axis representing amplitude (loudness) and the horizontal axis representing time. A louder sound will have a taller trace on the CRO, and a higher-pitched sound will have more waves packed together on the screen (shorter wavelength). The typical range of human hearing is from 20 Hz to 20,000 Hz (20 kHz).

An echo is simply a reflected sound wave. When a sound wave hits a hard, flat surface like a wall or a cliff, it bounces back. If the surface is far enough away, you will hear the reflected sound a short time after the original sound. We can use echoes to measure distances or the speed of sound itself. The key is to remember that the sound has to travel to the reflecting surface AND back again. Therefore, the total distance travelled by the sound is twice the distance to the object. The standard `speed = distance / time` formula is used, but you must be careful with the distance value. For example, if 'd' is the distance to a wall, the echo travels a total distance of '2d'.

Ultrasound is sound with a frequency above the upper limit of human hearing, which is about 20,000 Hz (or 20 kHz). Although we can't hear it, ultrasound has many important applications. Its high frequency means it has a short wavelength, which allows it to produce detailed images and be focused into narrow beams. Medical Uses: The most common medical use is in prenatal scanning to create images of a fetus in the womb. Pulses of ultrasound are sent into the body, and they reflect off boundaries between different tissues. A computer analyses the returning echoes to build a real-time image. It is used because it is non-ionising, meaning it doesn't carry enough energy to damage cells, making it much safer than X-rays for delicate tissues. It is also used to break up kidney stones. Industrial Uses: Ultrasound is used for industrial cleaning of delicate items like jewellery, and for quality control to check for flaws inside metal castings. Echo-sounding (Sonar): Ships use ultrasound to measure the depth of the sea or locate shoals of fish. A pulse is sent downwards, and the time taken for the echo to return from the seabed is used to calculate the depth.