SOUND

SOUND

Author: David Harrison

Updated: 10/07/01

School of Education and Humanities
Athrofa Addysg Uwch Gogledd Ddwyrain Cymru
North East Wales Institute of Higher Education
Wrexham, NORTH WALES

Galileo (early 1600s), the Italian famous for inventing the telescope, was the greatest contributor to our understanding of sound. He demonstrated that the frequency of sound was related to the perceived pitch by scraping a chisel across a brass plate causing a screech. The spacing of grooves in the scratch on the brass plate was related to the pitch. Leonardo da Vinci (1500) discovered the wave nature of sound. Mersenne (1640) first measured the speed of sound in air. Boyle (1660) discovered that sound must travel in a medium. Newton (1660s) demonstrated the relationship between the speed of sound with the density and compressability of a medium. Bernoulli (mid-1700s) showed that a string could vibrate at more than one frequency.

For a brief, but very useful, introduction to sound and sound waves visit Brainpop: sound where you will find a short animation with speech, so turn your speakers on, and a short quiz about sound. For another good introduction to sound visit Sound Waves at the Physics Education Laboratory at Virginia Tech.

Sound is an example of a longitudinal or compressional wave which is the physicists way of saying that it is a wave that causes a disturbance parallel to the direction in which the wave is moving, i.e., as a wave travels from left to right than the disturbance casued by that wave is in the left-right direction. Sound is a molecular disturbance and the disturbance is caused by a vibration. Whatever is vibrating, moving rapidly back and forth, sets up compressions and rarefactions which travel outwards from the object as a compressional wave. As sound waves are a disturbance or vibration in a medium of solid, liquid, or gas it follows that where there is no medium there is no sound " . . . in space no one can hear you scream . . .". Sound does not travel in a vacuum.

To see a software simulation of a longitudinal wave go to Waves. When looking at the simulation notice that in the lower diagram, "Progressive longitudinal wave", the red lines move from left to right and back again as the compressional waves travel from left to right, i.e., the disturbance is parallel to the direction of travel of the wave. Notice too that the lines are alternately closer together (compression) and further apart (rarefaction) as the wave travels. Also observe that although the wave travels form left to right, the particles of the medium, represented by lines, do not move overall as they are just disturbed about a mean position. The upper diagram represents a transverse wave, e.g., light. Notice that in a transverse wave the red lines move up and down, i.e., perpendidular, to the direction of travel of the wave which is from left to right.

By contrast light is a transverse wave in which the electromagnetic disturbance is perpendicular to the direction of travel of the wave and needs no medium to travel through, light travels in a vacuum.

The compressions and rarefactions of a compressional or longitudinal wave correspond to the peaks and troughs in a transverse wave. A compressional wave can be modelled using a "Slinky" toy.

The sounds we hear in our daily life commence as a vibration in an object, it may the plucked string of a guitar, the diaphragm in a loud-speaker, the vocal chords, a bell or whatever. The vibration, which can sometimes be seen, e.g., the vibration of a guitar string, may be amplified or modified, e.g., by the body of the guitar, and causes vibrations in the air which we pick up when they cause vibrations in the ear.

We can often feel the vibrations that cause sounds. Try a simple experiment: with your thumb and finger gently touch the skin either side of your throat at the front of your neck whilst making a vowel sound, e.g., aaaaaaaaaaaaah, you should be able to feel the vibrations of you vocal chords.

Sound, in common with other waves, is characterized by a frequency (f) or pitch and wavelength (l)and the relationship

velocity = frequency x wavelength

or v = f x l or f = v ÷ l or l = v ÷ f

is obeyed. The wavelength is the distance between successive compressions or rarefactions in the compressional wave and is measured in units of length, e.g., metres m. The frequency is the number of compressional waves passing per second and is measured in Hertz (1 Hz = 1 wave per sec)., e.g., middle C has a frequency of 264 Hz. The velocity of sound in air is approximately 330 m s^-1 (metres per second) at normal temperatures. For a simple guide to waves visit Brainpop: waves.

Try a simple exercise in numeracy: calculate the wavelength of middle C.

The human ear is sensitive to sounds of freqency 30 to 30 000 Hz, depending on the intensity, and is most sensitive to sounds of frequency 400 to 5000 Hz. At ages over forty a typical human suffers a progressive decay in high frequency hearing of about 160 Hz per annum.

When we listen to a tape recording of our own voice we are often amazed to hear how "thin" it sounds as compared to how we perceive our own spoken voice. When we hear ourselves speak we do so by air transmission of the sound from the mouth to the ear and also by bone transmission from the jaw to the ear and is the latter that is responsible for transmission of most of the low frequencies of the voice which decay more rapidly in air transmission. A tape recorder, or another person, "hears" our voice by air transmission only, thus a tape recording is deficient in low frequencies and lacks "body" and one’s own direct hearing is enriched in low frequencies which give it "body". However other people hear nothing wrong with our tape recorded voice.

To find out more about hearing visit Brainpop: hearing.

The velocity of sound depends on the nature of the medium through which it is travelling and because it relies on molecular disturbance it follows that when molecules are close together, as in a solid or a liquid, that sound travels rapidly but in a gas, in which the molecules are far apart, sound travels relatively slowly.

Notice that heavier molecules which are more resistant to disturbance, transmit sound waves more slowly, e.g., sound travels more slowly in carbon dioxide (molecular mass 44) than oxgygen (molecular mass 32), and in lead (atomic mass 207) than copper (atomic mass 64). Sound travels faster as the temperature increases, this is because molecules move faster as the temperature rises.

Because light travels very fast, almost instantaneously, it is possible to estimate the distance between an observer and a thunderstorm from the time difference between the lightning flash and the peel of thunderclap. The "rule of thumb" is that every five seconds time difference corresponds to a mile distance. Is this correct? In imperial units sound travels at approx. 0.2 mile/second (actually 0.214 mile/s) thus in five seconds 1 mile is covered by sound and the "rule of thumb" is about right (though intense rainfall, wind, and temperature will all affect the speed of sound).

The amplitude corresponds to amount of displacement of molecules by the sound wave and the human ear is sensitive to amplitudes in air corresponding to around a thousand millionth of a centimetre. The amplitude is directly related to the intensity of a sound wave which is the amount of energy transmitted by the wave and is expressed in watts/sq.metre.

The loudness of sound is largely subjective, the ticking of an alarm which is perceived as quiet during the day can seem annoyingly loud during the night as can a distant burglar alarm even though in reality the "noise" is small. Loudness is measured in decibels (dB) which is the ratio of the intensity of the sound to that of a standard sound of 0.000 000 000 001 watts/sq.metre at 1000 Hz which is just about the faintest sound that a typical young person can hear. A sound ten times as intense as this standard sound is rated at 10 dB or 1 B (Bel). The decibel scale is a logarithmic scale thus 11 dB is 10 times more intense that 10 dB and 15 dB is 100 000 times more intense than 10 dB.

Above about 130 dB the loudness of sound is progressively perceived as pain. Unwanted sound is noise. White noise is a mixture of all frequencies just as white light is a mixture all wavelengths (colours) of light. Noise is a by-product of energy conversion and is price we pay for a highly mechanised society, if you go into the African bush or Australian outback noise is not a great problem. Noise is probably the most pervasive form of pollution and can cause a great deal of anguish to some people whereas other people are unaffected. Legislation protects people from exposure to dangerous levels of noise and time limits are set for exposure to prescribed levels of noise and ear protectors must be worn in some occupations. "Personal Stereos" if played to loudly for too long periods can cause irreparable damage to hearing . . . basically if other people can hear your personal stereo then the volume setting is too loud and many "Walkmans" (Ó Sony Corporation) have automatic volume levels.

Sound like light can undergo reflection and refraction. Reflection of sound gives rise to the echo phenomenon which is reflected sound that can be easily distinguished from the original pulse of sound. It is necessary to stand about 16.5 metres from a large reflecting barrier to hear an echo. The sensation of sound persists for 0.1 second and the reflected sound must travel at least 33 metres (there and back) to be clearly separated from the original (assuming sound travels at 330 m/s). Clear echoes are heard when the sound is reflected of large, smooth, hard solid surfaces, e.g., walls, rock faces and echoes can be heard, for example, in caves, under large brick or stone bridges, from across narrow valleys, or in very large empty buildings (empty warehouse).

Many reflections from floors, walls and ceilings in a building gives rise to multiple indistinct echoes or reverberation which determines the acoustical qualities of auditoriums and concert halls. Too little reverberation gives a "dead" acoustic whereas too much reverberation "clouds" the sound to give a reverberant acoustic. Architectural acoustics are used to design halls that have the optimum reverberation times and much of the pioneering work was done by the American Wallace Sabine (1868-1919) and the Boston Symphony Concert Hall designed by Sabine is still considered as one of the world’s premier concert halls. The musical ambience of a room is determined not only by the walls, floor and ceiling but on the covering of the interior surfaces by fabrics, wood, plaster, acoustic tiles etc., soft surfaces absorb sound and deaden the acoustic whereas hard surfaces reflect the sound and liven the acoustic.

Refraction of sound waves is most noticeable when they travel obliquely from cold air into warm air and explains why sound travels great distances over frozen lakes. The sound travels upwards is refracted progressively by layers of warmer air above the lake and eventually is refracted back down towards the lake to be reflected upwards once more and the cycle repeats itself.

Most of us will have noticed that the pitch of the sound emitted by a moving object changes as the object passes us, e.g., the siren of an ambulance or fire engine or the whistle or horn of a locomotive. This change in perceived pitch in sound is known as the Doppler effect after the Austrian Scientist Christian Johann Doppler (1803-1853).

A simple analogy is to imagine a steady stream of equally spaced traffic passing a stationary observer. If the observer moves in the opposite direction to the traffic flow then the apparent frequency at which cars pass the observer increases. If the observer moves in the same direction as the traffic then the frequency at which cars pass the observer decreases. The actual frequency of the traffic does not change but the perceived frequency recorded by the stationary or moving observer does change.

The same principle applies to sound waves, a stationary observer hears the true pitch of a stationary sound source, an observer moving towards a sound source hears an increased frequency or pitch and an observer moving away from a sound source hears a decreased frequency or pitch. A moving sound source has an increased pitch as it approaches a stationary observer and a decreased pitch as it recedes from the observer. As the sound source passes the observer a drop in pitch occurs. It does not matter whether it is the observer or sound source that is moving, a Doppler shift in frequency will be heard when the observer and sound source are in relative motion, if they are closing there will be a Doppler increase in perceived pitch, if they are separating there will be a Doppler decrease in perceived pitch.

To understand how the Doppler effect arises you are advised to investigate the following simulations:

http://members.aol.com/nicholashl/waves/doppler.html for a very simple but clear animation that shows how the Doppler change in pitch arises and a similar animation is to be found at http://www.exploratorium.edu/xref/phenomena/doppler_effect.html.

http://www.sciencejoywagon.com/explrsci/dswmedia/soundwav.htm. For an interactive Doppler effect animation that allows you to investigate the effect of changing the speed of an object, the frequency of the sound and even the speed of sound. STOP the simulation and set the Speed of Object to 0.0 and then START. Notice how the compressional waves radiate evenly in all directions from the source (red dot) so that an observer placed anywhere around the sound source will encounter the same number of waves per second, i.e., they will hear the same pitch. STOP the simulation and use the mouse to drag the red dot to the left hand side of the screen and then adjust the Speed of Object to 0.2 and then START. What is different about the waves ahead of and behind the red dot now and will observers in front of and behind the sound source hear the same pitch? Increase the Speed of Object to 0.5 and then 0.8. What can you say about the magnitude of the difference in pitch before and behind the sound source as we increase the speed? Set the Speed of Object to the Speed of Sound, i.e., 1.0. What happens n

http://library.thinkquest.org/19537/java/Doppler.html is another Doppler animation that allows you to change the speed of an aircraft and to cause a sonic boom. However please not that the speeds (i) are given in mph (miles per hour) and (ii) are incorrect anyway as the speed of sound is not approximately 660 miles per hour (it's about 740 mph). But the animation is good.

http://calvin.stemnet.nf.ca/~dkeefe/lessons/doppler.html has a simple experiment to demonstrate the Doppler effect but you must be able to tie secure knots. I have tried it, it works!

The Doppler effect applies to all wave forms including light and is important in the study of atomic sized particles and distant astronomical objects. The universe in believed to be expanding at high speed because the pattern of spectrum of Fraunhofer lines in the spectrum of light from stars in galaxies other than our own is red-shifted as compared to the light from stars in our own galaxy. The redshift to longer wavelength can be explained by the Doppler effect: longer wavelength means lower frequency and a Doppler shift to lower frequency means that the objects are receding from us. Every galaxy shows this Doppler shift thus indicating that all galaxies appear to be moving away from us which can only be interpreted in terms of the universe expanding. The red shift has effect has shown that galaxies 1 000 000 000 light years distant, may be receding from the earth at 15000 km/s. If the universe is expanding now then if we could turn the clock back far enough then the universe would shrink back to a single point and the time at which the universe started to expnad from the point or singularity is the Big Bang. What we are not yet sure about is the rate at which the universe is expanding known as the Hubble constant. If we knew this we would know the age of the universe.

Other uses of the Doppler effect are in the radar surveillance of speeding cars and in marine navigation in which Doppler shifts of radio waves from orbiting satellites are used. Doppler shifts of ultrasounds are used in ultrasound body scans (especially during pregnancy) and in echocardiography (study of heart motion).

One of the principal means of communication is speech which is sound, in the form of language, that our aural senses are able to interpret. However even the biggest mouths are unable to project their voice very far (how far???). Speech can be made to travel great distances by converting the sound into electrical signals that can travel along wires and cables (or light signals down fibre optics) in telephone and telegraph links invented by Alexander Graham Bell or by conversion into a suitable radio-wave as pioneered by Guglielmo Marconi in his wireless telegraph system.

In radio transmission long wavelength sound waves (middle C is 1.2 metre wavelength) which do not travel very far are converted into a radio frequency electromagnetic wave that can travel over huge distances. The conversion of sound wave into radio waves starts with a microphone that converts sound energy (vibrations) into an electrical signal

For a simple guide to radio transmission and reception go to Brainpop: radio.

The electrical signal or wave is then combined with a carrier wave in a process known as modulation. For BBC Radio 4 on Long Wave the carrier wave is of frequency 198 kHz (or 1515 m wavelength). Waves can be added together or modulated in two ways either by amplitude modulation (AM) or frequency modulation (FM). In amplitude modulation the electrical signal from the microphone is a very variable amplitude wave which is combined with a the regular amplitude carrier wave to give a modulated wave. In frequency modulation it is the frequency that is modulated. AM radio can be transmitted over large distances (1 000 miles) but suffers from interference particularly from electrical disturbances (thunderstorms, electric motors, solar activity etc.) and the reception quality is often poor (not HI-FI!). FM radio is of high quality, free from most interference, and stereophonic (and digital) broadcast is commonplace however transmission is limited to distances up to only 15 to 50 miles and FM is only suitable for very high frequency radio signals hence the tendency to use the abbreviations VHF and FM interchangeably. AM radio in UK is found in the medium and long wave bands.

Examples of radio transmission data:

The next stage in the process is the transmission of the radio signal from an antenna as an electromagnetic waves. For efficient transmission the antenna must have a length corresponding to a multiple of one half wavelength of the carrier wave thus for Classic FM an antenna of approx. 1.5 m (4 ft 6 in) should be suitable. For Radio 4 a 707 m antenna would be impractical and quarter length Marconi antenna with the ground serving as the other quarter wavelength is used.

The radio receiver or radio (or wireless) contains a receiving antenna or aerial in which the modulated radio carrier wave induces an electrical signal, typically 50 mV in a AM radio, and this signal is then demodulated and amplified. The listener must tune the radio so that the appropriate carrier wave is demodulated, i.e., the carrier signal removed to reveal the original waveform.

The final stage in the process is conversion of the demodulated electrical signal into acoustic energy or sound which is accomplished by a loudspeaker or speaker. The speaker carries out the reverse process to that of the microphone. Speakers and microphones convert electrical signals to mechanical vibrations or vice versa and are examples of transducers. Both comprise a diaphragm that vibrates by either by receiving acoustic energy (microphone) or by movement of an electromagnetic coil arising from an electric signal (speaker).

Ultrasonics is the study and application of ultrasound which are "sound" waves with frequencies above human perception. Ultrasound has a wide range of industrial and medical applications:

• ultrasonic cleaning
• ultrasonic welding of metal and plastic
• ultrasonic pile driving
• ultrasonic drilling (of glass)
• ultrasonic scanning of opaque materials
• ultrasonic ocean bed mapping by sonar
• ultrasonic detection of flaws (cracks, dislocations, blowholes) in solids
• ultrasonic smoke particle precipitation
• ultrasonic atomization of liquids and metals
• focussed ultrasonic shattering of gall and kidney stones
• ultrasonic pressure relief in eye of glaucoma sufferers
• ultrasonic echocardiography (see Doppler effect)
• ultrasonic foetal monitoring during pregnancy
• ultrasonic skin examination of burn victims to locate healthy tissue
• ultrasonic examination of tumors and cysts
• ultrasonic physiotherapy and massage.

In many cases the utility of the ultrasound arises from localized heating or fluid motion or agitation or bubbling brought about by dissipation of the ultrasound energy. 1 MHz ultrasonic waves dissipate about half their energy to the surroundings over a distance of 20 m in water. Ultrasound travels at approximately the same speed as ordinary sound, e.g., 1500 m/s in water and ultrasound obeys the laws of refraction and reflection. In addition to travelling through opaque materials, ultrasound can be made to travel along the surface of a solid as Rayleigh waves and this technique is used in electromagnetic signal processing.

Ultrasound is produced by applying an alternating voltage across opposite faces of crystals or plates of piezoelectric crystals e.g., quartz or piezoelectric ceramics, e.g., barium titanate or lead zirconate. The applied voltage causes pulsation (expansion/contraction) of the crystal at the same frequency as the alternating voltage. This phenomenon of piezoelectricity was discovered by Pierre and Paul-Jacques Curie in the 1880s. If the frequency is carefully chosen the pulsations become very large and the crystal or plate exhibits resonance and emits large amounts of ultrasonic waves. The piezoelectric effect is also used in your quartz watch, a voltage is applied to the crystal which pulsates at a precise frequency so ensuring that your watch keeps good time. In piezoelectric gas lighters (in gas fires and gas ovens) the reverse effect is used a crystal is "squeezed" and becomes electrically charged and creates a spark which lights the gas.

 Please send comments, suggestions to:

Dr David Harrison(harrisond@newi.ac.uk)

Dr Clive Buckley(Buckleyc@newi.ac.uk)

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Updated 10 July, 2001

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