Energy is transmitted from one place to another in two ways. In the first, the object itself travels from one place to another and the energy goes with it, as with a bullet that has come out of a gun, or a stone that has been thrown. In the second, energy reaches one place from another through a wave.
For example, if we throw a stone into the middle of a still pond, the kinetic energy that was in the stone produces a vibration in the molecules of the water of the pond. The wave produced by that vibration is transmitted towards the bank of the pond. While the water wave is being transmitted, the molecules of the water vibrate up and down, but the transmission of the wave is from the middle of the pond towards the bank. When the wave reaches the bank, the water can be seen splashing at that place. In this way the wave carries the kinetic energy that was in the stone from the middle of the pond right to the bank. This is why a wave is a means of transmitting energy.
Read that paragraph once more and notice the strange thing hidden inside it. The wave goes from the middle of the pond all the way to the bank, but the water does not. Each bit of water only bobs up and down in one spot and stays there. So what exactly is it that moves across the pond? Only the pattern, and the energy the pattern is carrying. You can test this without any equipment at all. Drop a leaf onto a still pond and then drop a stone some distance away. The ripples will race outwards and pass right under the leaf, and the leaf will rise and fall as each one goes by, but it will not be carried to the bank. It stays where it was. That is the whole idea of a wave in one sentence: a wave moves energy from place to place without moving the stuff it travels through. Once you have that, everything else in this topic is detail.
Types of wave
Some waves need a medium in order to be transmitted, and some do not. On this basis waves are of two types, mechanical waves and electromagnetic waves.
| Wave | Splits into | Which splits further into |
|---|---|---|
| WAVE | Mechanical wave (needs a medium) | Longitudinal wave and Transverse wave |
| Electromagnetic wave (needs no medium) | Light waves, X-rays, radio waves |
A wave that needs a medium in order to be transmitted is called a mechanical wave. A wave that does not need a medium in order to be transmitted is called an electromagnetic wave. Light waves, X-rays and radio waves are electromagnetic waves. On the basis of the direction of transmission of the wave and the direction of the vibration, waves are of two types, transverse waves and longitudinal waves.
The split between mechanical and electromagnetic sounds like bookwork until you ask one question. Between the Sun and the Earth there is almost nothing at all, no air, no water, no solid. Yet sunlight crosses that emptiness every day and arrives here in about eight minutes. Sound could never do that. If the Sun exploded you would see it, but you would never hear a thing, and neither would anybody else, because a sound wave needs particles to pass the disturbance along and out there are almost none to pass it. That is what a medium means, and that is why light gets a whole separate branch of the family tree. Astronauts working outside their spacecraft can see each other perfectly well but cannot hear each other at all, so they speak by radio, and radio waves work out there for the same reason light does.
Transverse wave
A wave in which the particles of the medium vibrate at right angles to the direction in which the wave is transmitted is called a transverse wave. The wave produced in water is a transverse wave. A transverse wave is transmitted by forming crests and troughs. In the same way, light waves and radio waves are also transverse waves.
Longitudinal wave
A sound wave is a longitudinal wave. In a longitudinal wave the direction in which the wave is transmitted and the direction in which the particles of the medium vibrate are one and the same. A wave in which the particles of the medium vibrate to and fro along the very direction in which the wave is transmitted is called a longitudinal wave. A sound wave is a longitudinal wave. In the same way the vibration that occurs in a spring, and ultrasound, are longitudinal waves.
Do not try to remember two separate definitions, because there is really only one question and the two answers to it. Ask: which way do the particles wobble, compared with the way the wave is going? If they wobble across it, at right angles, the wave is transverse. If they wobble along it, backwards and forwards, the wave is longitudinal. That is the whole difference. And it explains why the two kinds look so different when you draw them. A transverse wave has room to go up and down, so it makes the hills and valleys we call crests and troughs. A longitudinal wave has nowhere to go except forwards and backwards, so instead of hills it makes places where the particles are bunched up and places where they are spread out. Crest and compression are the same idea in different geometry, and so are trough and rarefaction.
How sound travels through air
When sound energy is being transmitted, the region in the air where the molecules are crowded together is called a compression, and the region where the molecules are far apart from each other is called a rarefaction. One compression (C) and one rarefaction (R) together make one complete wave of sound. As shown in the figure, when a sound wave is transmitted the molecules in the air vibrate to the left and to the right, and the sound energy is also transmitted in that same direction.
Look carefully at that figure, because it shows something quite surprising about hearing. Nothing travels from the loudspeaker to the ear except a pattern of crowding and spreading in air that was already there. No air is delivered to your ear. The air near the speaker is pushed forward, it crowds the air next to it, that crowd pushes the next lot, and the squeeze passes along the room like people jostling in a queue, while each person stays roughly where they were standing. When the crowded part arrives at your eardrum it pushes it inwards a little, and when the spread out part arrives the eardrum springs back out. In and out, thousands of times a second, and that tiny drumming is everything you hear. All of music, all of speech, every voice you know, is just air being crowded and uncrowded against a small piece of skin.
Some terms related to waves
| Term | What it means | Symbol and SI unit |
|---|---|---|
| Crest | The part of the wave that has risen above the mean position of the particles of the medium | - |
| Trough | The part of the wave that has gone below the mean position of the particles of the medium | - |
| Amplitude | The maximum displacement of a particle of the medium from its mean position | a, in metre (m) |
| Wavelength | The distance from the highest point of any one crest or trough to the highest point of the nearest next crest or trough | λ (lambda), in metre (m) |
| Complete wave | The part of a wave made by one crest and one trough together, or by one compression and one rarefaction | - |
| Frequency | The total number of waves formed in unit time | f, in hertz (Hz) |
| Wave velocity | The distance covered by the wave in unit time | v, in metre per second (m/s) |
Mathematically, the product of the frequency and the wavelength is the velocity of the wave.
| \( v = f \times \lambda \) |
Say the two quantities out loud in words and the formula writes itself. Frequency is how many whole waves go past you each second. Wavelength is how long each one of those waves is. So if four waves go past every second and each wave is three metres long, then twelve metres of wave has gone past you in that second, which means the wave is moving at twelve metres per second. Waves per second, multiplied by metres per wave, gives metres per second. The units themselves are telling you to multiply. And notice what falls out of this at once: for a given speed, a longer wave must arrive less often and a shorter wave must arrive more often, because the two have to multiply to the same total. Long wavelength goes with low frequency, and short wavelength goes with high frequency.
Worked example: finding a frequency
If a certain wave has a speed of 10 m/s and its wavelength is 1 m, what is its frequency?
| Step | Working |
|---|---|
| Given | v = 10 m/s, λ = 1 m, f = ? |
| Formula | \( v = f \times \lambda \) |
| Rearrange | \( f = \dfrac{v}{\lambda} \) |
| Substitute | \( f = \dfrac{10}{1} = 10 \) Hz |
So the frequency of the wave is 10 Hz, which means ten complete waves are produced every second. You can check this in words without the formula at all. Each wave is one metre long and the wave is covering ten metres every second, so ten of them must go past in that second.
The velocity of a sound wave
The velocity of a sound wave is different in different media. The velocity of sound is greatest in a solid medium. After that it is in a liquid, and it is least in a gaseous medium.
Most people guess the opposite. Air feels empty and easy to move through, and a wall feels solid and blocking, so surely sound should race through air and struggle through stone? It is the other way round, and the reason is worth understanding rather than memorising. A sound wave travels by each particle nudging the next one along. In a gas the particles are far apart and hardly connected, so a particle must drift a long way before it meets its neighbour, and the message is slow. In a solid the particles are packed close together and firmly linked, so the moment one moves its neighbour feels it immediately, and the nudge is passed on almost at once. Liquids sit in between. This is not just theory. If you put your ear against a long metal pipe or a railway track, you can hear a tap from far away arrive through the metal noticeably before the same tap arrives through the air. Careful: the fact that sound travels fast through a wall does not mean it travels loudly. Some energy is lost at each surface, which is why you hear the neighbours as a muffled rumble rather than clear words.
Amplitude and how loud a sound is
Think about what happens when a drum set is struck gently with a stick and when it is struck hard. Both make a sound, and both make the same note, but one is far louder. Striking harder means giving more energy to the drum skin, so the skin is pushed further from its mean position before it springs back. A larger displacement from the mean position is exactly what a larger amplitude means. So a hard strike produces a wave of large amplitude, and we hear that as a loud sound. A gentle strike produces a wave of small amplitude, and we hear that as a soft sound. Amplitude carries the energy of the wave, and it is what your ear reports as loudness.
Frequency is a completely separate thing, and it is easy to mix the two up. Frequency is how many waves arrive each second, and that is what decides whether a sound is high or low, not whether it is loud or soft. A thin tight guitar string vibrates many times a second and gives a high note. A thick loose string vibrates fewer times a second and gives a low note. You can play either of them loudly or softly by plucking harder or more gently, which changes the amplitude while leaving the frequency alone. So amplitude decides loudness, and frequency decides pitch.
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