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Hearing things - Physics narrative
Physics Narrative for 5-11
A Physics Narrative presents a storyline, showing a coherent path through a topic. The storyline developed here provides a series of coherent and rigorous explanations, while also providing insights into the teaching and learning challenges. It is aimed at teachers but at a level that could be used with students.
It is constructed from various kinds of nuggets: an introduction to the topic; sequenced expositions (comprehensive descriptions and explanations of an idea within this topic); and, sometimes optional extensions (those providing more information, and those taking you more deeply into the subject).
Imagine you're working at your desk upstairs. You become distracted by a news programme from a downstairs radio: starting to pay attention you realise that you can clearly hear every single word.
Not surprising in some ways… but then again there's something rather fundamental to notice here. The sound starts from the radio's speaker downstairs and reaches you at the top of the house. The sound travels up the stairs, back along the landing and then up along another set of stairs to your lair. Not only could you hear the news up-stairs and down-stairs, but you could probably hear it outside as well.
In day-to-day living we are surrounded by all kinds of different sounds. Just stop and listen. The lived-in world is awash with sounds: noise; music; speech; birdsong. Some of these, such as the noise from traffic or the sound of people talking or the radio playing are just there and we often don't even notice them. Of course, sounds don't just exist as a kind of backdrop to our lives. They also provide us with information. For example, you quickly learn to recognise, by the sounds, when bacon is cooking too quickly, when the kettle is coming to the boil or when the car is misfiring.
How are we able to hear?
Vibrations from source to detector – that's how we hear.
So, how is it that you are able to hear the radio playing in all parts of the house or the bacon sizzling or the notes from the guitarist at a concert? The guitarist is up there on the stage and you are in the audience. What happens to allow you to hear the sounds from the guitar, which is at least 20 metres away?
The first step in answering this question is to treat the act of hearing as involving a chain from source (which is vibrating) to medium (which enables the vibrations to pass) to detector (which in this case is you!) For vibrations to travel from source to detector there must be particles of matter in the gap, and these form the medium. If there are no particles then there is nothing to carry the sound from source to detector.
The medium transmits information from the source to the detector.
As we hear, information travels from source to detector
Source and detector
All sources of sound have the same kind of to and fro motion. All sources of sound vibrate. It is an interesting exercise to think of a sound (yes, any sound!) and trace it back to the vibration that is producing it.
Here are some examples: voice, vibration of vocal cords; notes from a Sitar, vibration of a string; toot of a trumpet, vibration of lips at mouthpiece.
The vibrating source acts on the medium around it, setting the medium moving to and fro, in a way that matches the motion of the source.
The detector also vibrates as it is set in motion by the medium adjacent to it. The motion of the detector matches the to and fro motion of the medium, so the sound is carried from source to detector – transmitted by one block of particles acting on the next.
Density varies as the vibration travels
What happens in the medium to allow the sound to pass? If the medium is air, the air particles are initially in a state of random motion.
Here we show what happens as the cone of a loudspeaker acts on the air in front of it. As you can see, the to and fro motion of the loudspeaker cone produces changes of density in the air.
As the cone moves forwards, the air particles are squashed together to make a region of high density. As the cone moves backwards, the air particles in front of it spread out to form a region of low density.
The animation helps to visualise the patterns of high and low air density. These are first created directly in front of the loudspeaker cone and then further away, as the disturbance in one 'block' of air affects the next 'block' of air. In this way the sound travels out from the loudspeaker cone through the surrounding air.
What sound is
A crucial point to understand here is that as the disturbance of high– and low-density regions travels out through the air, each block of air simply moves backwards and forwards following the motion of the loudspeaker cone. If you're not sure about this, step back to the previous screen and review the animation there. Each block of air moves backwards and forwards. It is not the case that the block of air that starts directly in front of the loudspeaker cone ends up at your ear. The sound travels through the air but the air itself simply moves backwards and forwards.
You might ask the question:
Teacher: But what exactly is the sound?
Well, as we've emphasised, the cone moving to and fro is not the sound. Rather it is the source of the sound.
Equally, the detector is not the sound.
The sound is actually the disturbance travelling through the air, the to-and-fro motion of the air that creates the pattern of high– and low-density regions. That is what we detect with our ears.
The human ear
The way in which humans hear is rather complicated, and explaining it fully involves aspects of physiology, psychology and acoustics. A simpler description concentrates on the action of the ear as it converts sounds to a sequence of nerve impulses which are transmitted to the brain. The ear's ability to do this allows you to detect, all at once, a range of sounds, from loud to soft and from a high-pitched squeak to a low-pitched growl.
The ear consists of three parts: the outer ear, the middle ear and the inner ear. Each part serves a specific purpose in the task of detecting and interpreting sound.
The outer ear collects and channels sound to the middle ear. The middle ear transfers the to and fro motion of the air (which is the sound) into matching vibrations of the bone structure of the middle ear. These vibrations are transmitted into a to and fro vibration in the fluid of the inner ear. This vibration is changed into nerve impulses, which are then transmitted to the brain as electrical signals.
The board game
Mouse Trap provides a good basis for imagining how the ear works.
Describing what you can hear
Range of sounds
The range of sounds that humans are able to hear is impressively large, taking us from the loud roar of an aircraft as it makes its final approach on landing to the quiet murmur of the wind as it passes through the trees. Alternatively we might think in terms of moving from the low pitched rumble of distant traffic to the high-pitched screech of the dentist's drill.
We can consider these two ranges of our hearing as forming two sides of a
- From very quiet to extreme loudness.
- From a low-pitched rumble to a high-pitched squeak.
Pitch and frequency
Hearing different notes
People vary in their ability to detect the pitch of a sound. For example, in tuning a guitar, some are able to distinguish easily between two notes of similar pitch while others can't hear the difference. A more objective measure than pitch is frequency, measured in hertz (Hz).
The frequency of any vibration is defined as the number of complete vibrations made each second: the frequency (hertz) is equal to the number of vibrations per second.
Sometimes a complete vibration is referred to as a cycle: the frequency (hertz) is equal to the number of cycles per second.
You can picture one vibration or cycle of the speaker cone being completed as it starts from its most forward position, moves backwards, and then moves forwards to return to its original position.
The frequency value not only specifies the number of complete vibrations made by the source each second, but also the number of regions of high (or low) density produced in the medium each second. In other words, it gives the frequency of the actual sound.
High pitch corresponds to high frequency, low pitch to low frequency. There is a whole spectrum of sounds arranged along the frequency axis.
More on frequency
Quite often the numbers get large, and the frequency is referred to in terms of kilohertz (kHz): 1000 hertz is the same as 1 kilohertz.
For example, a hi-fi loudspeaker might have a range of 20 hertz to 20 kilohertz and so be capable of producing sounds over our whole range of hearing.
In 1939 musicians moved to an agreement on standard pitch. Middle C (called that because it is a note around the middle of the piano keyboard) is 256 Hz and concert A (the note the orchestra tunes to before the show begins) is 440 Hz.
The frequency doubles for every octave upwards.
Loudness and amplitude
What does the loudness of sound depend on?
Sounds vary not only in terms of the pitch or frequency, but also in their relative loudness.
As you might expect, louder sounds are produced by larger vibrations of the source. If the loudspeaker cone moves backwards and forwards over a greater distance, a bigger disturbance is produced in the air and a louder sound results.
As with pitch, the loudness of a sound is a subjective measure – it depends on the person. You may have an elderly relative who listens to the TV at what seems to be ear-shattering volume to you, and yet is comfortable for their ears. The same sound is judged to be of different loudness by two people.
A more objective measurement of loudness is the amplitude of the vibration.
The human ear is sensitive to sounds over a huge range of loudness. For example, the loudest sound that the ear can safely detect without suffering any physical damage is more that one billion times more intense than the threshold of hearing (where sounds can just be heard).
The ear responds to sounds of different loudness in such a way that huge increases in amplitude are registered as small increases in loudness.
The decibel scale
To match this way in which the ear responds, the relative loudness of sounds is usually measured in decibels.
The decibel scale, which is a logarithmic scale, stretches from 0 dB at the threshold of hearing to 140 dB at the threshold of pain (values vary, as this is subjective – pain is not a precisely defined experience). Each time you go up one decibel, the loudness of the sound increases by a constant factor and you can just about hear this change.
Logarithmic intensity scales are also used to report on the perceived brightness of light (the sensitivity of the eye is also logarithmic) and for measuring the strength of earthquakes (the Richter scale).
Speed of travel
Echoes, imaging and measurement
Clap your hands not too far from a big wall and you can hear both the original clap and, shortly afterwards, its echo. What is happening here is that the sound takes one path straight from your clapping hands to your ear (a short distance), while another path involves the sound starting off from your hands, reflecting off the wall and then travelling back to your ears (a somewhat greater distance).
In fact, these are just two of the many paths followed by the sound as it travels out in all directions through the surrounding air.
By measuring the total distance travelled (from your hands to the wall and back) and timing the gap between the original clap and you hearing its echo, it is easy enough to get a rough value of the speed of sound in air.
Depending on the accuracy of your timing, you are likely to find a value of about 300 metre / second. In textbooks the value of the speed of sound in air is often quoted as 340 metre / second.
Under normal conditions, this speed remains pretty well constant. However, since the motion of the sound depends on the movement of air particles, the speed of sound does change with temperature because this determines how fast the particles are moving.
If we assume that the speed of sound is 340 m s-1, we have a way of measuring distances. This is used in sonar measurements.
Timing lots of pulses in a cunningly planned pattern can give an ultrasound scan. With really careful and fast processing of these signals you can get a real-time image, of, for example, a baby in a womb.
Bats use ultra-sonic (too high a frequency for us to hear, but good for the bats) pulses to navigate with. It's possible to imagine that they
see the world very differently from us.
Speeds of sound in different media
Physics Narrative for 5-11 11-14
Sounds in solids, liquids and space
Sound can travel through any medium, so long as there are sufficient particles in each cubic metre to allow the to and fro motion of one block of particles to be passed on to their neighbours.
Solids, liquids and gases differ in the arrangements of their particles and in the forces between the particles. So you might expect variations in both the speed and range of sounds travelling through them, since both depend on how the disturbance passes on from one block of particles to the next.
Sounds travel faster and farther in solids. Presumably this fact must have been well known to all of those who put their ear to a rail track to detect whether or not a train was coming.
In liquids sounds also travel over great distances at considerable speed. This is apparent from listening to whales as they communicate with one another. The complexity of the paths which these vibrations follow is exploited by Tom Clancy in his book
The Hunt for Red October, where he makes much of the difficulties involved in interpreting sonar signals while tracking submarines.
In deep space there are only about 3 particles of hydrogen per cubic metre and this is not enough to sustain a sound. Disappointingly the
booms of space movies are a fiction! All explosions in outer space take place in eerie silence. As the
Alien movie tells us:
In space, no-one can hear you scream.
The speed of sound varies in different media. Here are some typical examples: in air, 340 m s-1 ; in water, 1500 m s-1 ; in steel, 6000 m s-1.
All around you there is plenty of evidence that different frequencies of sound travel at the same speed. The very existence of music depends on this. If the notes of differing frequencies, from different instruments, arrived at your ears all at different points in time, the effects would probably be rather unpleasant!
Working with sounds
Sound consists of audible vibrations, which travel from a source to a detector. These can be of a whole range of frequencies and a whole range of amplitudes. We hear these as sounds of different pitches and different loudnesses. Sometimes one sound will be made up of many of these frequencies at once, each with their own amplitude. All of these contribute to the amplitude of the sound, as well as its characteristic quality.
These vibrations travel at one quite constant speed, about 340 metre / second in air, whatever the frequency or amplitude. Sound travels through solids and liquids at higher speeds.