AS 2 Physics High
Diffraction
This section will cover the following topics:
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Diffraction
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Diffraction Around An Object
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Diffraction Effects
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Radio and TV Broadcasts
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Diffraction Through a Single Slit
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Diffraction Through Two Slits
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Diffraction Grating
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Acoustic Room Design
Diffraction
Have you ever wondered why you can hear someone who is round the corner of a building, long before
you see them? It appears that sound can travel round corners and light cannot. What is the reason for
this? Do light and sound share any properties that might cause this effect?
Diffraction Around An Object
Waves can 'spread' in a rather unusual way when they reach the edge of an object - this is called
diffraction. The amount of diffraction ('spreading' or 'bending' of the wave) depends on the wavelength
and the size of the object. Diffraction can be clearly demonstrated using water waves in a ripple tank.
Have a look at this a simulation of a ripple tank containing an object which obstructs the propagation of
a wave:
The key to understanding diffraction is understanding how the relative size of the object and the
wavelength affect what goes on. By examining the three diagrams, decide which of these statements is
correct:
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Which of these is true:
a)When the wavelength is bigger than an obstacle, then the sound waves bend around the obstacle.
b)When the wavelength is smaller than an obstacle, then the sound waves bend around the obstacle.
(Answer is a)
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Which of these is true (applying these rules to sound waves rather than water waves):
a)Behind a barrier, the sound which has the longest wavelength compared to the size of the obstacle
will sound quietest.
b)Behind a barrier, the sound which has a shortest wavelength compared to the size of the obstacle will
sound quietest.
(Answer is b)
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Which of these is true:
a)Behind a barrier, the sound which has a longest wavelength compared to the size of the obstacle will
be loudest.
b)Behind a barrier, the sound which has a shortest wavelength compared to the size of the obstacle will
sound loudest.
(Answer is a)
True or False:
"The amount of diffraction that occurs depends on both the size of the obstacle and the wavelength of
the sound."
a) True
b) False
(Answer is a True)
Our simulation shows that with a 'long' barrier, there's a lot of reflection of incident energy back
towards the source, but although there is some diffraction or bending of the wave around the barrier,
this still leaves a 'zone of silence' behind it. However with a short barrier (the same length as the
wavelength) diffraction is very effective and there is almost no zone of silence behind it.
From this, we can reach the conclusion that with sound waves, it is the low frequencies (which have
long wavelengths) which diffract around corners. You can experiment with this by listening to traffic
noise from a busy road from 'around the corner' of a building (not in direct line-of-sight to the traffic),
and then moving to a location a similar distance from the road but in direct view of the passing cars.
The 'swish' of the tyre- and wind-noise contains a lot of high frequency energy, and you should find
that this does not diffract around the corner as effectively as the 'rumble' of engine noise.
Diffraction Effects
At high frequency, when the wavelength is small compared to the object size, then the sound does not
diffract very effectively. In acoustics, we use the term "shadow zone" to describe the area behind the
object, because if you stand there, you are in an 'acoustic shadow' (just like the 'optical shadows' we see
on those rare occasions when the sun comes out) and the sound is quieter than elsewhere. This is
exploited in acoustics to reduce noise levels. For instance, noise barriers can be put up alongside major
roads - houses behind the barriers are exposed to less noise if they are in the shadow zone (but
remember - low frequencies are unaffected by the barriers and can diffract over the top). Look out for
heavily-built fences along the side of motorways in built-up areas - these are noise barriers. Sometimes
the barriers are made of earth, in which case they're called a 'bund' (really, they are!).
A really good example of diffraction can be seen with another type of wave barrier - a harbour or dock
wall. If you live near the sea, have a look at waves on a windy day hitting a harbour wall. Some of the
energy will reflect, but at the end of the barrier (near the opening of the harbour) the waves will 'bend
around' and come inside. Think about it...if this did not happen, and the water inside the harbour stayed
dead calm, then somewhere near the harbour mouth you would see completely 'flat' water immediately
next to very 'wavy' water. This can't happen - the wavy water has to transmit its energy into the flat
water - and this is another way of picturing the 'bending' which diffraction describes.
Going back to acoustics - you might want to avoid this shadowing effect when you go to see a band or
orchestra play...especially if it's a 'standing' gig and you're not so tall. If you're behind someone taller,
then not only do you not get to see the musicians, you also get less direct sound from the stage because
it has to diffract around the head (and perhaps hat) in front. Seats in theaters and stadia are 'raked' not
only because it gives you a good line of sight, but also because it improves the sound quality.
Light waves have a very small wavelength (typically 500nm, although of course it changes with colour)
and so do not diffract noticeably. We can set up specialised experiments in the lab to demonstrate light
diffraction, but if you're on the beach and someone is standing in your sun, diffraction around the
'obstruction' is not going to get you a tan. We've been using sound as an example since it has a much
longer wavelength (from a few centimeters to a few meters depending on the frequency) and so objects
such as the edges of walls will cause diffraction and enable sound to travel round corners.
Diffraction also plays an important role in allowing us to locate sources of sound. If you close your
eyes, you can tell which direction sound is coming from. How does this work?
When sound reaches you from straight ahead, the same sound signal is received at both ears. This is
because the head is more-or-less symmetrical and the sound to both ears travels an identical path
length. Your brain uses this information to locate the sound in front of you.
When sound comes from the side (directly, or via a reflection as shown above), the sound at each ear is
different. Sound to the furthest ear has to diffract (bend) around the head. This means the sound wave
arrives slightly later and is altered in terms of the balance of high and low frequencies it contains (we
could call this a spectral alteration). As we have seen, sounds with short wavelength (high frequency)
don't diffract as well, so the furthest ear hears less high frequencies. The brain senses this difference in
arrival time and frequency content, and uses it to locate sound.
Try locating sound sources with a finger in one ear and your eyes shut. Make sure no-one is around to
watch you do this, unless you have previously warned them what is about to happen...
Radio and TV Broadcasts
Diffraction also affects the way in which electromagnetic (radio) waves are broadcast and received for
radio and TV signals.
TV and VHF radio signals have wavelengths of around a few meters. This means they cannot diffract
over hills or large buildings. The receiver must be in direct line-of-sight with the transmitter. Repeater
stations are often positioned at the top of hills to reach all the houses in the valley that would otherwise
be in the 'shadow' of the hill.
Long-wave radio is sent using waves with a much larger wavelength of around 1km. This means they
can diffract around objects including hills and buildings; they can reach places that short-wave radio
cannot. This is why it is often possible to listen to long wave radio stations such as radio 4, even when
FM reception is poor. It's also why stations on long wave (BBC Radio 4 - 198LW) are tuned to the
same frequency wherever you go - there's only one transmitter for the whole of England, Wales and
Ireland (at Droitwich).
By contrast, FM transmitters only cover a small region - to see what frequencies BBC stations are
broadcast on in your area, check out http://www.bbc.co.uk/radio/frequencies/ . This limited coverage is
why you have to continually re-tune a car radio when listening to FM on a long journey...although if
you have an 'rds' radio, it does this for you.
Question: Why can't BBC Radio 1 be broadcast on 98.9 FM over the whole country, using a large
number of local transmitters all tuned to the same frequency? (Hint - think about superposition, and
constructive and destructive interference).
Diffraction Through a Single Slit
These diagrams are just a guide - below is a proper mathematical ripple tank simulation of waves
passing through a slit. What difference does the length of slit make in terms of diffraction?
When the gap size is larger than the wavelength, the wave passes through the gap and does not spread
out much on the other side. When the gap size is equal to the wavelength, maximum diffraction occurs
and the waves spread out greatly - the wavefronts are almost semicircular.
Huygen's Principle
One way to explain the effects of diffraction is to use a mathematical method invented by Christiaan
Huygens (14th April, 1629 - 8th July, 1695); a Dutch mathematician and physicist.
Huygens argued that a wavefront could be modeled as a series of wavelets. A wavelet can be described
as a circular- shaped wave much like the ripple you would get from dropping a small pebble into a
pond. These wavelets superimpose and interfere to form more complicated wavefronts. For example if you dropped a number of pebbles in a straight line, all 'in one go' at exactly the same time, a 'straight'
(in science-speak plane) wavefront would be created. The diagrams below show Huygen's principle in
action:
Young's Experiment
So far we've only considered the case of a single slit or gap for the wave to pass through. What happens
if there are two or more slits? We'll end up with two or more diffracting waves, which we might expect
to interfere with one another...
Below in a simulation of diffraction through two slits. The experiment is named after the guy who first
carried it out - Young's double slit experiment. Have a look at what is happening to the right of the slits.
Is there a pattern? Is the amplitude larger at some places than others?
To the right of the slits, the waves interfere with each other. In fact, you can generate the same patterns
by placing two sources where the slits are. The sound through each slit diffracts and radiates rather like
two 'point sources'. So the patterns you are observing are very similar to those for two sources whose
wave radiation interferes together.
Think back - if we are dealing with the interference of two sources, there will be places where the
waves are in phase and cause constructive interference, and other places where the waves are out of
phase and interfere destructively. In an audio example, the two slits could be replaced with two
loudspeakers, and the maxima and minima in the wave superposition would then correspond to
locations of loudness and quiet.
We'd hear these loud / quiet areas one after another as we moved in an arc in front of the loudspeakers they're called 'Young's fringes'. If the experiment is carried out using light waves, you get bright
locations for constructive interference and dark locations for destructive interference. Young used this
experiment to measure the wavelength of light.
Diffraction Grating
What happens when we increase the number of slits in Young's experiment? In that case we create
something called a diffraction grating. Again, we can think of the diffraction grating as being the same
as a set of sound sources which are all coherent with each other. We now have a case where there are
many more than just two sources interfering. The simulation below shows the sound field generated by
a set of sources. Do we just get a chaotic mess? Are there still quiet and loud patches - 'Young's
fringes'?
We don't just end up with a chaotic mess - because the sound sources are coherent. So we still get 'loud
spots' where the sound from the slits arrives in-phase, and 'quiet spots' where the sound from the slits
cancels due to destructive interference. As with Young's double slits, the directions of the fringes can be
calculated. Note however that once we get to a reasonable distance from the grating, towards the right
of the simulation window, the waves from each slit have added back up into a large plane wave by
Huygen's principle.
In acoustics, the most common example of many sources side by side is a column loudspeaker. These
are the tall narrow speakers that you may have seen used for speech reinforcement in your school or
church. Here the designer makes use of the interference pattern to ensure that sound spreads out
broadly in the horizontal plane, but forms quite a tight 'beam' in the vertical plane. This only works
when the column in placed vertically, and means that the sound is well-distributed around the audience
but does not radiate into the roof space of high buildings (especially sports halls, churches and railway
stations etc) and 'bounce around' causing too much reverberation.
In large PA systems for outdoor gigs, a similar arrangement is popular. Modular speaker boxes are sat
one on top of another in a tall 'pile', or hung from a suspending gantry. This is called a 'line array', and
follows the same idea. The sound is directed broadly in the plane of the audience's heads - but forms a
tight 'beam' in the vertical plane. This means that if the line array angled slightly towards the ground,
the audience can enjoy high-volume music - but that the spread of this music to surrounding houses etc
is controlled by the line array direcitivity. Trying to control noise 'pollution' is one of the major
problems you have to overcome if you want to run a music festival...unless you can persuade your
audience to travel somewhere really remote, you risk annoying the neighbours, an without proper
acoustic design that can get you shut down.
Acoustic Room Design
Let's come back 'indoors' and think about the many different types of buildings which need to have
special acoustic design. In concert halls, recording studios for music, TV and radio, and even classrooms we need to control the amount of sound reflected from the walls, floor and ceiling. These
reflections disturb the original sound and cause unwanted echoes and reverberation. In concert halls
and class-rooms these echoes mean that the original sound can become 'difficult to hear properly' there can be poor intelligibility. (You may suspect some of your teachers suffer from this at the best of
times, but too much reverberation can only make things worse!).
Try this experiment - go into a small bare room (like a toilet, unless you have luxury furry wallpaper
and a deep-pile carpet...) and make noise - a handclap will do. The direct sound arriving at your ears
directly from your hands is quickly followed by reflections from the walls, ceiling and floor. These
reflections can cause the sound to be 'coloured', or to put it another way, the timbre of the sound will
change. (Timbre is a French word which describes sound 'quality', and is pronounced 'tambruh', not
'timber'! The German equivalent is useful too - 'klangfarbe' or literally, 'tone-colour'.) In extreme cases
reflections can also cause the sound image to appear to come from the 'wrong' direction.
The diagram below shows a plan view of a small rectangular room, highlighting a first order (involving
only one reflecting surface) reflection from the top wall in red. In small rooms, first order reflections
tend to be loud and arrive very soon after the direct sound. You can imagine the waves bouncing around
like balls on a pool table - second order reflections are like shots played off two cushions, third order
off three etc etc. The higher-order the reflection, the further the wave has travelled and the later they
arrive. These later reflections all blend in together, and cause reverberation.
There are two basic forms of acoustic treatment to deal with reflections, namely absorption and
diffusion.
Absorption
One solution to reflections is to apply absorption to the wall, which turns acoustic energy into heat this is a kind of damping. This absorption can be a specialist product such as those made of mineral
wool, open cell foam, or recycled fibrous material like paper-waste, but absorption can also be
provided by more commonplace object such as curtains, sofas or carpets. It can be a tricky balance for
an acoustic designer - too much absorption, and the room will sound 'dead'. The sound quality would be
like listening outdoors, where only the direct sound from a source is heard (assuming 'soft' ground and
an absence of nearby buildings). While a few people favour such acoustic 'non-environments' for
mixing music, for most people these are rather oppressive spaces too far removed from normal
listening conditions.
So - what other tricks can the acoustic designer use?
Diffusion
Acoustic Diffusers are used to disperse reflections spatially - to 'spread out' reflected sound energy over
a wide range of angles - as shown in the diagram above. Some diffusion can be obtained by carefully
placing book cases and other furniture in a room, but often specialist (=expensive!) diffusing surfaces
can achieve greater diffusion in a more controlled manner. By using sound diffusers, first order
reflections are dispersed to be heard later by the listener, and by removing and delaying early
reflections, diffusion and absorption can make a small music studio sound like a larger room.
Consequently, design is all about locating the reflection points for first order reflections, and applying
appropriate treatment there.
Test
1. What can we say if the vibrations in a wave are at right angles to the direction of travel?
a) It must be a transverse wave.
b) It must be a longitudinal wave.
c) It must be a sound wave.
2. What can we say if the vibrations in a wave follow the same direction as the direction of travel?
a) It must be a transverse wave.
b) It must be a longitudinal wave.
c) It must be a light wave.
3. The distance from the crest of one wave to the crest of the next wave is called:
a) The amplitude
b) The wavelength
c) The frequency
4. What is the unit of frequency?
a) m/s
b) s
c) Hz
5. Which is the correct equation?
a) wave speed = frequency x wavelength
b) wave speed = frequency + wavelength
c) wave speed = frequency ÷ wavelength
6. What happens when waves bounce off a barrier in a ripple tank?
a) They are reflected.
b) They are refracted.
c) They are diffracted.
7. What happens when waves change direction going over a barrier in a ripple tank?
a) They are reflected.
b) They are refracted.
c) They are diffracted.
8. What happens when waves spread out going through a gap in a barrier in a ripple tank?
a) They are reflected.
b) They are refracted.
c) They are diffracted.
Answers
1. a, when waves travel at right angles they are known as transverse waves
2. b, when the vibartions follow the same direction as the travelling waves it is a
longitudinal wave.
3. b, the wavelength is the measure of one complete cycle of the wave from one
crest to another.
4. c, The unit of frequency is Hz
5. a, The speed of wave is the product of frequency and wavelength
6. a, The waves are reflected back when they bounce off the ripple tank
7. b, In the process of changing direction the waves get refracted.
8. c, When waves try to spread themselves out of a gap they tend to get diffracted.