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Learn about waves, their representation on graphs, speed calculations, characteristics, and practical applications like sonar and ultrasound imaging in this comprehensive guide.
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What is a wave? A wave is an oscillation that moves through space, transferring energy from one place to another. Which of these is not an example of a wave? All true waves move or propagate through space, therefore the ripples on a sand dune are not waves.
Representing waves There are two main ways of representing a wave on a graph. • graphing an oscillation in time: amplitude y t period This graph represents how y changes with time. It could be an oscillation of voltage, displacement, pressure, or any other suitable variable, depending on the context.
Representing waves There are two main ways of representing a wave on a graph. • graphing an oscillation in space: amplitude y x wavelength This graph represents how y changes along an axis x in space. It could be a wave of displacement or pressure, or any other suitable variable, depending on the context.
Waves in time and space These two waveforms look the same, but they each give different information about the wave they represent. amplitude y t period amplitude y x wavelength Always label your axes!
Studying waveforms in the classroom An oscilloscope is an instrument that detects a varying voltage from an input, such as a microphone, and plots its waveform against time. A signal generator produces an alternating voltage at a chosen frequency and amplitude. It can also produce a range of different waveforms.
Wave speed A series of surface waves is moving across a pond. The peaks of the waves are 20cm apart. A duck is disturbed by the waves and bobs up and down twice a second as the waves move past it. At what speed are the waves travelling across the water surface? wave speed = number of waves passing per second × wavelength wave speed = frequency × wavelength The waves are passing the duck at a rate of 20 × 2 = 40cm/s This formula can always be used to find wave speed.
Waves in a medium Most types of waves are disturbances that propagate through a medium. Sound waves travel through the air as variations in pressure and density. Can sound travel through any other medium? Transverse waves can travel across a water surface. These are known as surface waves. Longitudinal pressure waves can also travel through a body of water. During an earthquake, transverse and longitudinal waves travel through solid rock away from the epicentre. What is the difference between a sound wave and a pressure wave?
Pitch and loudness The shorter the wavelength of a sound, or the higher the frequency, the higher the pitch to the human ear. The loudness of a sound depends on the amplitude of the wave. Which of these traces shows the louder sound and which shows the sound with the higher pitch? higher pitch louder Not every note of the same pitch sounds the same. The waveform of a wave determines the quality of the sound.
What is ultrasound? The range of human hearing is 20–20,000Hz. Any sound above 20kHz is called ultrasound. Whales and dolphins communicate using ultrasound. Many of them also use it for echolocation. Echolocation works by timing how long a wave takes to reflect from a surface and return to its source. That information is then used to calculate the distance it has travelled. Animals are thought to do this naturally, but it can also be done by a computer, such as in prenatal scanning.
Sonar One practical application of ultrasound is sonar. Originally an acronym for ‘SOund Navigation And Ranging’, sonar uses the same principle as echolocation in animals. A signal is sent out, and the time taken for it to return to its source after reflecting from a surface, such as a lake bed, is measured. Knowing the speed of sound in water, it is then possible to calculate the distance the sound has travelled using this equation: distance = speed × time
Depth evaluation using ultrasound A ship has recorded the following trace while using sonar to map the bottom of a lake. The traces are 0.01s apart, and sound travels at 1500m/s in water. How deep is the lake? reflected signal transmitted signal distance = speed × time = 1500 × 0.01 = 15m However, this is not the depth of the lake! This is the distance the sound has travelled, down to the lakebed and back up again. depth of the lake = 15 2 = 7.5m
How does ultrasound imaging work? We have seen how to calculate a simple distance to a boundary using sonar. How can ultrasound be used to create more complex images, such as of an unborn child? Waves are not only reflected from solid surfaces: they are reflected from any boundary between different media. When transmitted into the body, ultrasound is reflected to varying degrees by all the different tissue boundaries present. The reflected waves are detected by a receiver. A computer turns the distance and intensities of these echoes into a 2-dimensional image.
Further uses for ultrasound Ultrasound has many uses in industry as well as medicine. Jewellers and watch repairers use ultrasound to clean delicate items. The dirt is shaken off by the air vibrations, leaving the mechanism unharmed. The reflection of sound waves from any boundary also makes ultrasound useful for finding flaws in mechanical structures or the raw materials used to build those structures.
Describing diffraction When waves pass through a gap they diffract. This means they spread out on the far side of the gap, changing shape as they pass through it. • Maximum diffraction occurs when the gap size is equal to the wavelength of the waves. • If the gap is much smaller than the wavelength, the waves cannot pass through the gap at all. • If the gap is muchlarger than the wavelength, only the edges of the waves diffract. When waves pass an obstacle on only one side, only those edges are diffracted.
Using diffraction Diffraction is useful for long distance communications. Long wave radio waves are diffracted by hills and mountains because the wavelength is of a similar size to the obstacle. This allows them to travel around these obstacles, providing coverage over a large area. Higher frequency waves are diffracted much less. Television signals, for example, have a much shorter range.
Interference of sound What caused the pattern of loud and quiet spots? Both speakers produce identical sounds. When the sound from one speaker meets the sound from the other, the two waves interact with each other. This is known as interference. If the waves are in phase, they reinforce each other. If the waves are out of phase, they cancel each other out. + + = = This is destructive interference. This is constructive interference.
Using interference The phenomenon of interference has many uses. Some car manufacturers put microphones into the engine bay, delay the sound by half a wave, and play it back to the passengers. The effect of this is that the noise of the engine is cancelled out, and the journey is much quieter. The same idea is used on helicopters, to remove the incredibly loud rotor noise and allow the pilot to communicate more effectively.
Polarization Electromagnetic waves (such as light) ‘oscillate’ in three dimensions, shown by the green and the blue waves below: unpolarized wave polarized wave polarizing filter When these waves pass through a polarizing filter, only one plane is able to get through (the blue one in this case). The other parts of the wave are blocked. This is polarization. If another slit at 90 degrees is placed in the waves path, then none of the wave can get through.
Polarization of light In 1938, Edwin Land developed the polaroid lens. Today they are used in most sunglasses, as well as microscopes and LCD screens, but they were originally used to help with fishing! On a sunny day, light reflecting from a water surface can cause glare. However, only light in one plane is reflected from the flat surface of the water. Polaroid sunglasses are designed to block out this light, making it much easier to see the fish clearly.
Sending signals into space Some radio waves follow the contours of the Earth. These are called ground waves. These are typically waves with a frequency of 3–3,000kHz because their long wavelength means they diffract around the curves of the Earth’s surface. Radio waves that refract through the ionosphere and return to Earth, giving the impression of reflection, are called sky waves. Their frequencies are 3–30MHz. At frequencies over 30MHz, radio waves can pass completely through the ionosphere and into space. These are called space waves.
Communicating with satellites Space waves are used to communicate with satellites. These waves are known as microwaves because of their short wavelength compared to other radio waves. Microwaves only diffract by a small amount due to this short wavelength, so they can be sent to a satellite in a thin beam to save energy. The satellite can then send a second beam back to earth in response. Radio waves with a frequency of greater than 30GHz are easily absorbed and scattered by dust and water in the atmosphere, so they have little practical use.
Identifying wave behaviour What is happening to the radio signals in this picture?
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