SOUND WAVES including ultrasound and earthquake waves

Sound waves - properties explained, uses of sound including ultrasound

Doc Brown's Physics Revision Notes

Suitable for GCSE/IGCSE Physics/Science courses or their equivalent

This page will answer many questions e.g.

 Why is sound a longitudinal wave?

 Why can't sound travel through a vacuum?

 Know that and understand that sound waves and some mechanical waves are longitudinal, and cannot travel through a vacuum.

Describe an experiment to measure the speed of sound.

What are the uses of ultrasound?  Why can some earthquake waves be the same as sound waves?



The characteristic properties of sound waves longitudinal waves

Sound waves are caused by some object or material vibrating e.g. your vocal chords vibrating, plucked guitar strings, something grating on a surface, the diaphragm (cone) moving back and forth in a loudspeaker etc.

The vibrations from a sound source are carried along by any available medium - gas (e.g. air), liquid (e.g. water) or solid (e.g. wall).

Sound cannot travel in a vacuum of empty space - there is no material to vibrate.

You can do a simple experiment with an electric ringing bell paced in a large bell jar attached to a pump.

As you pump out the air, the sound of the bell gets fainter and fainter until you can't hear it as the medium is removed from around it. However, you can still see the striker of the bell vibrating.

BUT, what exactly happens to the medium and enables it to convey the energy of a sound wave?

The above diagram gives an idea of a longitudinal wave of sound where the oscillations are in the direction the wave moves.

The oscillations in the same direction as the wave progression, can be considered as vibrations or disturbances in the medium through which the sound wave is travelling.

Reminder: Contrast this oscillation with transverse waves like water waves or electromagnetic radiation where the oscillations are at 90o to the direction of wave movement.

These oscillations in longitudinal sound waves show areas of compression and rarefaction.

A compression is where the particles of the medium are compressed to a maximum and a rarefaction is where the particles of the medium are spaced out the most.

When the particles get squeezed closer together or spaced apart more than 'normal' they will want to return to their rest position. This they do, driving the wave in a forward direction. So the wave is a continuous series of compressions and decompressions (rarefactions) in which the particles pushed together and then spaced apart again.

In the diagram above for longitudinal sound waves, wave B has twice the frequency and half the wavelength of wave A.

Reminder of the general wave equation applied to sound:

speed of sound wave (m/s) = frequency of sound (Hz) x wavelength of sound wave (m)

in symbolic 'shorthand'    v = f x λ, rearrangements:  f = v λ   and   λ = v f

Sound waves that we hear travel at the same speed whatever the frequency, so, with reference to the diagram, if the speed stays constant and you halve the wavelength, you must then double frequency for the equation to be valid.

Where the vertical lines are close together you can imagine the particles in a material being compressed closer to one another (compression) and where the lines are spaced well apart, so are the particles of the medium (the rarefaction).

The frequency of a sound wave (or any wave) equals the number of compressions passing a point per second, and is perceived as the pitch eg of a musical note.

The frequency of sound is the number of vibrations per second (unit hertz, Hz).

The amplitude is the maximum compression with respect to the 'rest line' and is perceived as loudness.

The 'rest line' is effectively the point of no disturbance, zero amplitude - neither compression or rarefaction.

 

The diagram above illustrate the simulation of sound waves by push and pulling on a slinky spring to create pulses of energy being transmitted along the slinky spring (the 'medium'). Its a good simulation of the compression and rarefaction behaviour of a longitudinal wave.

 

Unlike electromagnetic light waves, sound cannot travel through empty space (vacuum) because you need a material substance (gas, liquid or solid) which can be compressed and decompressed to transmit the wave vibration.

The more dense a material, the faster the sound wave travels.

Therefore in general for sound: speed in solids > speed in liquids > speed in gases

This is borne out by the data of sound speeds quoted below:

Typically at room temperature, the speed of sound waves in various materials at ~20-25oC

air 343 m/s (0.34 km/s),

that's why if a thunderstorm is 1 km away, you hear the thunderclap about 3 seconds after the flash of lightning - the speed of light is so much greater than the speed of sound that the flash is virtually instantaneous

water 1493 m/s (1.49 km/s),  sea water 1533 (1.53 km/s), high velocity useful in sonar scanning of sea bed

kerosene 1324 m/s (1.32 km/s) (liquid hydrocarbon)

ordinary glass 4540 m/s, pyrex glass 5640 m/s (5.64 m/s)

iron 5130 m/s (5.1 km/s), steel 5790 m/s (5.8 km/s)

rocks 2000 to 7000 m/s (2-7 km/s), the speed tends to be greater in the more dense igneous rocks compared to less dense sedimentary rocks.

for comparison:

longitudinal earthquake P-waves typically travel at 2 to 7 km/s depending on whether the wave is in the Earth's crust, mantle or core and the speed will also depend on density and temperature

 


Reflection, refraction and diffraction of sound waves

Reflection of sound waves

When sound waves meet a barrier they can be reflected just like any other wave (diagram of wavefronts on the right). The angle of incidence will equal the angle of reflection (with respect to the normal at 90o to the boundary). Any solid surface will reflect sound, though soft material will tend to absorb the sound wave energy.

A flat hard smooth surface is the best reflector of sound waves - think of echoes (reflected sounds) that permeate an empty house with no carpets laid down.

A soft rough surface is the best absorber of sound wave energy - the idea is used in recording studios to minimise unwanted sounds and in ear muffs to protect you from ear damage due to very loud sounds.

Refraction of sound waves  (same diagram of wavefronts as for reflection)

At the same time as reflection, if the sound waves can penetrate the material at a boundary, it will change speed if the second medium is of different density. Therefore the sound waves will change direction, that is the sound waves are refracted. If the sound waves pass into a more dense material they will bend towards the normal.

Although they are longitudinal sound waves, this is normal wave behaviour just as you see with experiments with transverse light waves or water waves.

The frequency of does not change in passing from one medium to another, but if the speed changes, so must the wavelength.

speed of sound wave (m/s) = frequency of sound (Hz) x wavelength of sound wave (m)

Therefore at constant frequency the wavelength is proportional to the speed of the sound wave.

So as the wavelength gets longer (the waves stretched out), the wave moves faster.

The shorter the wavelength of the sound wave (waves come closer together) the slower the wave.

This is why sound wave undergo refraction at a boundary between two different media.

 

 

Diffraction of sound waves

Diffraction is the effect of waves spreading out when passing through a gap or passing by a barrier. In effect, waves go round corners! and it doesn't matter if its sound, light or water waves - they all diffract and bend round corners!

You should appreciate that significant diffraction of sound waves only occurs when the wavelength of the sound wave is of the same order of magnitude as the size of the gap or obstacle.

A: There is a relatively small diffraction effect when sound waves pass through a wide gap that is much bigger than the wavelength of the sound wave.

B: You get the maximum spreading or diffraction when the waves pass through a gap of similar size to the wavelength of the incident sound waves.

 

A little calculation to do with diffraction

speed of sound wave (m/s) = frequency of sound (Hz) x wavelength of sound wave (m)

Therefore wavelength =  λ = v f

(i) A typical audible frequency might be 2 kHz, 2000 Hz

Speed of sound ~340 m/s

Therefore λ = v f = 2000 / 340 = 5.9 m

(ii) The musical note 'middle C' has a frequency of ~262 Hz

Speed of sound ~340 m/s

Therefore λ = v f = 262 / 340 = 0.77 m

The second wavelength is similar to the width of a doorway.

Sound will travel throughout a house by both reflection and refraction!

 


Sound and human hearing

Your ear is designed to collect sound and cause the eardrum to vibrate. These vibrations are conveyed to the ossicles (tiny bones) and through the semi-circular canal to the cochlea. It is the cochlea that turns these vibrations into electrical nerve signals which are sent to the brain for interpretation. From these nerve impulses of varying frequency (pitch) and amplitude (loudness, intensity) your brain builds you a 'sound picture' of speech, music etc.

 

We experience longitudinal waves as sound, but we can only hear a relatively narrow range of frequencies.

What sound frequencies can we hear and why?

What we can hear as human beings is limited by the size and shape of the eardrum and anything else that is connected and vibrates - resonating with the eardrum. The ossicles, the bones of the middle ear only function well over a limited frequency range. We cannot hear very low pitched or very high pitched sounds.

The bones are most efficient at transmitting frequencies of around 1000 Hz to 3000 Hz (1-3 kHz)

Younger people have a much greater hearing range which can be as wide as 20 Hz (0.02 kHz) to 20 000 Hz (20 kHz).

Unfortunately, as you get older, the upper frequency limit decreases AND your sensitivity decreases - you become harder at hearing. This is unavoidable wear and tear of the cochlea or auditory nerve.

A personal note (if you pardon the pun!)

The cochlea of my left ear never developed correctly, and so, although all the bones are there and presumably vibrate, no nerve signals are generated, so I've always been deaf in my left ear. My deafness was spotted by a primary school teacher when I was 10 and duly tested to confirm I was indeed deaf in my left ear. I didn't know anything different to monophonic sound, so I've never known what stereophonic sound sounds like! My loving parents didn't seem to realise it either, even though my deafness got me into trouble! One line in my school report, as regards homework, read "plays on his deafness", brilliant eh! It has had very amusing consequences for my classroom teaching (many years ago!). If there was a bit of nonsense on the left at the back of the lab, I always enquired to the right and entirely blamed the wrong group. The students thought this most amusing with many giggles and sniggers and I was regarded as a bit eccentric. Since I couldn't resolve the problem, I once more 'played on my deafness' and accepted at times I'd never find the culprits and sought 'diplomatic' and 'amicable' solutions and survived to teach in comprehensive schools for over 28 years!

 

Sound is important to human hearing - a means of communication via speech, enjoyment of music etc.

Your ear drum resonates with a sound wave hitting it and via some bones and nerve receptors, 'sound impulses' are transmitted to the brain.

This is clear example of yourself appreciating energy transfer by sound waves - greatly appreciated by somebody who is deaf in one ear!

Another good example, which I'm glad to say I have not encountered, is the enormous power of earthquake P-waves - a huge amounts of energy can be conveyed many miles through the Earth's crust, mantle and even through the core. However,

 

Sound waves are produced by mechanical vibrations (e.g. musical instruments) and travel through any medium, gas, liquid or solid, but not vacuum, where there is nothing to vibrate!

In music, if a middle C tuning fork is struck, the two prongs vibrate from side to side 262 times every second ie middle C has a frequency or pitch of 262 Hz.

The pitch of a sound is determined by its frequency and loudness by its amplitude.

The rest line is represented by the horizontal red line on the CRO diagrams below.

The four pictures could represent the sound waves of musical notes recorded by a microphone, converted to an electronic signal and displayed in wave form on an oscilloscope screen (CRO). You can produce a wide range of frequencies using a signal generator and they can be converted into sound waves.

Note that ...

The shorter the wavelength the higher the frequency (or pitch) of the sound.

The higher the waveform (greater the amplitude) at the point of maximum compression, the louder the sound - and conveying more energy.

So, we can interpret the four signals as follows:

1. has the smallest amplitude, the softest note (opposite of loudest) - just a whisper!

2. has the largest amplitude, the loudest note - a good shout out loud!

3. has the longest wavelength, lowest frequency, lowest pitch e.g. a low note sung by a base singer.

4. has the shortest wavelength, highest frequency, highest pitch, e.g. a treble note or a squeaky animal.

 


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Echoes are reflections of sounds

Sound waves are reflected of hard flat surfaces eg walls, but tend to be absorbed by rough soft surfaces eg like foam -used in ear protectors.

Note the difference in echoes between an empty bare room in a house and when it is carpeted and filled with furniture and curtains etc.

Echoes are heard when you shout towards a hard flat surface and you then hear the reflected sound waves impacting on your inner ear drum.

The further away a reflecting surface is, the longer the time interval between your shout and hearing the echo.

If the wall or side of a mountain or valley is 340 m away, its 2 seconds before you hear the echo (speed of sound 340 m/s).

If the reflecting surface is a km (1000 m) away, its about 6 seconds before hear the echo.

speed = total distance / total time, time = distance/speed, time = 2000/340 = 5.9 s

You can hear sounds from some distance throughout a building or even a wide area outside because the sound waves are reflected and bounced around by all hard flat surfaces BUT sound waves are also diffracted and can therefore bend round corners into your ear!

The further away you are from the sound source, the fainter it will sound for two reasons:

on every reflection some of the sound wave energy is absorbed

(ii) waves naturally spread out from a central source.

 

Echoes can be used to measure the speed of sound in air (next section).


Experiments to measure the speed of sound

(a) Synchronised microphones

The experiment is performed by connecting a loud speaker to a signal generator to generate the sound to be picked up by the microphones.

You select a particular known specific frequency e.g. 250 Hz (f in Hz).

Two microphones are connected to an oscilloscope which pick up the sound from the speaker and which is converted to an electrical signal by the microphone and displayed as a trace on the cathode ray oscilloscope screen.

You can secure the speaker and two microphones with stands and clamps making sure they are aligned at the same height.

You set up the oscilloscope to detect the sound wave signals from both microphones - to give you two traces on the screen.

You start with the two microphones close together.

You then slowly move one microphone away from the other.

When the two microphones are first exactly one wavelength apart, the two signal traces on the oscilloscope are exactly aligned - synchronised, as in the diagram above.

You then measure the distance between the microphones and this gives you the wavelength of the sound.

This is because the sound waves are aligned so that they are just one wavelength apart.

speed of sound wave (m/s) = frequency of sound (Hz) x wavelength of sound wave (m)

in 'shorthand'    v = f x λ

you know the frequency in Hz from the signal generator setting

and the wavelength is the distance between the microphones in cm ==> m

 

You repeat the experiment to calculate the average wavelength to give statistically the best result.

You can then repeat the experiments with other frequencies from the signal generator.

 

(b) Echo method

-


ULTRASOUND

As already mentioned, you can use a signal generators to produce electrical oscillations of any frequency. These are converted to produce mechanical vibrations.

These sound waves can be produced to well beyond the range of human hearing.

These high frequencies are above 20 kHz (20000 Hz) and are known as ultrasound.

Ultrasound of very high frequency sound waves are used in scanning pregnant women to monitor the progress of unborn baby.

The ultrasound waves enter the woman's body and the echoes-reflections and refractions are picked up by a microphone and converted into electronic signals from a which an internal picture can be constructed.

This is considered a safe technique for pre-natal scanning of a foetus and much safer than using dangerous X-rays.

Tissues or fluids of different density give different intensities of reflection and so differentiation of the structure of the womb, foetus or baby can be seen - modern ultrasound scanners can produce quite high resolution images.

So how does ultrasound scanning work?

When sound waves (in this case ultrasound) are passing from one medium to another (solid or liquid - body fluid, tissue, bone, organs etc.) some are reflected, and some are transmitted and refracted at the boundary interface (see right diagram).

The time for reflections to take place at a particular angle is measured i.e. the time it takes for the sound impulses to be emitted from the transmitter and reflected back off a boundary and the return signals picked up by the detector. The recorded data is processed by a computer to build up a 3D video on the screen from which individual images can be viewed and even printed out (for medical checks-investigation and hopefully for the delight of expectant parents).

This form of medical imaging works because ultrasound waves can pass through the body but if they meet a boundary e.g. between fluid and tissue some of the waves are reflected. It is the distribution of these echo signals that enables the computer to build up the image.

 

Industrial uses of ultrasound

Ultrasound is used to detect flaws in manufactured products such metal castings or pipes.

If there is a flaw in the casting or the welding of an object, when scanned with ultrasound the flaws show up as some of the waves are reflected-deflected where you might expect them to go right through the object.

 

Use of ultrasound for sonar - echo sounding

Ultrasound systems are used by small boats, ships and submarines for echo sounding.

From the echo signals you can get the distance to the seabed.

With more sophisticated systems you can get an 'underwater picture' of what's there e.g. shoal of fish, sunken wreck, dangerous underwater rocks.

 

See questions in the next section


Calculations involving waves

Be able to use both the equations below, which apply to sound waves (and their rearrangements):

appropriate units used in ()

a) sound wave speed (metre/second, m/s) = frequency (hertz, Hz) x wavelength (metre, m)

in 'shorthand'    v = f x λ

rearrangements:  f = v λ   and   λ = v f

b) sound wave speed (metre/second, m/s) = distance (metre, m) / time (second, s)

in 'shorthand'    v = d t

rearrangements:  d = v x t   and   t = d v

This is the general formula for the speed or velocity of anything moving.

(a), (b)

 

Q1 A musical note has a frequency of 300 Hz.

If the speed of sound in air is 340 m/s calculate the wavelength of the note.

λ = v f = 340 / 300 = 1.13 m (3 s.f.)

 

Q2 A pulse of ultrasound from a fishing boat takes 1.40 seconds to travel from the boat down to the seabed and back to the 'microphone' detector.

If the speed of sound in seawater is 1530 m/s calculate the depth of the water at that point.

speed = distance / time, rearranging gives d = s x t,

but you halve the time t to 0.70 seconds because of the double journey (there and back) of the wave.

Therefore depth = 1530 x 0.70 = 1070 m (3 s.f.)

 

Q3


Earthquake Waves

When an earthquake happens in the Earth's crust it results in the spreading out of seismic waves. They result from the huge amounts of potential energy stored in the stressed layers of rock resulting from plate tectonic movement. These earthquake waves can be detected all around the world using an instrument called a seismometer.

The speed of seismic waves depends on the material they are travelling through, in particular the density of the rock layers. When the waves meet a boundary they may be partially reflected, completely reflected, absorbed, continue in a direct line with a different speed or the waves might be directed and change direction.

Because the density of the rock changes gradually in a particular layer, so does the speed of the wave. If refracted, the waves follow curved paths (see the diagram below). However, at a boundary, the speed may change more abruptly giving a bigger change in direction (just as you see with light ray experiments with prisms.

Scientists (seismologists) study the properties and pathways of seismic waves to deduce the internal structure of the Earth.

These seismologists calculate the time it takes for these shockwaves to reach every seismometer around the world and, importantly for a specific earthquake, observing the parts of the Earth's surface where you don't detect the waves.

 

There are three types of earthquake waves (seismic waves)

P-waves are longitudinal waves and so can travel right through the Earth to the other side of the world.

They are also called primary or compression waves and are identical to sound waves but with much longer wavelengths - see calculation below.

P-waves travel at ~5 to 8 km/s in the crust, mantle or core and ~1.5 km/s (the same as 'sound' in water!).

Weak to moderate earthquake waves have a frequency of 0.1 to 2 Hz on the surface.

If a seismic wave has a speed of 5 km/s (5000 m/s) and a frequency of 0.5 Hz

the wavelength = λ = v f = 5000 / 0.5 = 10 000 m (10 km), ~1000 x more than our audible sounds

S-waves are transverse waves and can only travel through solids, so they cannot travel through the core.

S-waves cause an 'up and down' shearing movement of the rock layers at 90o to the direction of the wave.

L-waves are transverse move along the surface of the Earth moving the ground up and down.

For more details see earthquake (seismic) wave analysis notes in Earth Science section

P-waves (primary waves) and S-waves take curved paths because of the ever changing density of the Earth's layers producing a gradual refraction effect.

The longitudinal P-waves can pass right through the centre of the Earth but due to refraction give two small shadow zones (marked black on the diagram). They travel faster than S-waves.

The transverse S-waves are absorbed by the outer core and give one much larger shadow zone (marked blue + black on the diagram). They travel slower than P-waves.

You get much greater refraction effects at the boundaries between the crust/mantle, mantle/outer core and outer core/inner core.

Seismometers pick up the vibrations of earthquake waves from many seismographic stations around the world (over 2000 locations).

Analysis of the paths of waves in terms of velocity and direction data has enabled geologists to work out the basic layered structure of the Earth.

From the speed, absorption and refraction of seismic waves scientists have worked out the number and depth of the four layers of the internal structure of the Earth.

e.g. from the shadow zones you can work out the depth of the mantle and the inner and outer layers of the core.

 


Check out your practical work you did or teacher demonstrations you observed in Unit P1.5, all of this is part of good revision for your module examination context questions and helps with 'how science works'.

demonstrating transverse and longitudinal waves with a slinky spring

demonstrating the Doppler effect for sound.


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Waves - electromagnetic radiation, sound, optics-lenses, light and astronomy revision notes index

General introduction to the types and properties of waves and how to do wave calculations, ripple tank experiments

Illuminated & self-luminous objects, reflection of visible light, ray box experiments, ray diagrams explained, uses of mirrors

Refraction and diffraction, the visible light spectrum, prism investigations, ray diagrams explained

Electromagnetic radiation, sources, types, properties, uses and dangers

The absorption and emission of radiation by materials - temperature & surface factors

See also Global warming, climate change, reducing our carbon footprint from fossil fuel burning

Optics - types of lenses (convex and concave), experiments and ray diagrams

The visible spectrum of colour, light filters and explaining the colour of objects

Sound waves - properties explained, uses of sound including ultrasound, earthquake waves

See also more detailed notes on The Structure of the Earth and earthquake waves (seismic waves)

The electromagnetic spectrum and astronomy - solar system, cosmology, nuclear fusion and the life cycle of stars

The Big Bang Theory of the Universe, the red-shift and microwave background radiation


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