Physics - EMR, radiation and sound

Achievement Standard and links to past papers here (I suspect this link will be dead now the standard has expired).
Note: This Achievement Standard has expired but I have left the material up because it may be of use for other science courses (I will likely appropriate parts of it as material for the new ESS standard on Physical Processes on the Earth.
I have been aware of some editorial activity since the standard expired. Some of this is useful but it would be courteous to contact me prior to editing, or I will need to lock this page.
If you print or distribute material from this wiki it would also be courteous to contact me.

Video - discovery of the electron: This is number 2 of a series of 15 and some of the others may be useful also.

This achievement standard covers Electromagnetic Radiation (EMR), radoactive decay and its products, and sound and ultrasound. For EMR and sound it looks at the wave properties of these phenomena, including wavelength, frequency and speed relationships, and related properties such as pitch, how these waves propogate and so on. For radioactive decay, it covers alpha, beta and gamma radiation, their properties and decay products.

Section 1: Waves - an introduction

Ocean swells near Lyttleton
Waves consist of energy propagated through a medium (matter or space) in the form of a regular cycle between two different energy types.
Examples include:
  • sound waves: the energy changes between elastic potential energy and kinetic energy (it is the same for seismic waves)
  • water (ocean or fluid) waves: the energy changes between gravitational potential energy and kinetic energy
  • electromagnetic waves oscillate between energy stored in magnetic fields and energy in electric fields.
In the case of all types of wave, the nature of the oscillation causes the wave-front to move along through whatever medium is carrying it (only EMR can move through empty space). A single "wave" by itself is called a pulse or a soliton. Under certain circumstances a wave can be fixed in place; this is called a standing wave.

Wave terms

A wave can be represented with a sine function:
The wave illustrated above is described as a transverse wave. The displacement direction is perpendicular to the direction of travel. EMR has mostly transverse properties.
Waves can also be longitudinal:
In these waves, the direction of movement of the wave front is parallel to the direction of movement of the wave. The waves consist of compressions (particles compressed and closer together) and rarefactions (particles further apart). Sound waves and seismic P waves are examples. Click here for an animation of these.
Note that a graph of pressure against displacement perpendicular to the wave fronts would produce a sinusoidal function similar to the graph above.

The Wave Equation:

For all waves, there is a relationship between the wavelength and the speed of the wave and how many waves pass a given point per unit time. The relationship is given by the equation:
  • v is the speed of the wave, in metres per second
  • f is the frequency of the wave, in cycles per second (Hz)
  • λ (Greek letter lambda) is the wavelength (distance from crest to crest) in metres.

Speed: Sound waves vary in speed, depending on the medium, temperature and other factors. EMR always travels at the 'speed of light', which is a constant given the symbol 'c'. The value of c is 3 x 108 m s-1 .
Because all EMR travels at c, the wave equation from above becomes
c = f λ
for any problem involving EMR in empty space or air (but may be different if the EMR is refracted, i.e is in glass or water).

Frequency: The frequency of a wave is how many waves (per second) pass a particular point. For example, the note ‘A’ on a piano produces 440 waves per second. We say that its frequency is 440 ‘per seconds’. The ‘per second’ is a unit with a special name; we call it a hertz, symbol Hz – so concert A is 440 Hz. If you had a tuning fork of this freqency, the prongs would vibrate 440 times per second.

Period: this is the time between two waves and is thus the reciprocal of frequency: T = 1/f, where f is the frequency in Hz and T is the period in seconds. If the freqency was 50 Hz then the period is 1/50 second or 0.02 seconds. You can calculate the period by typing the frequency into your calculator and pressing the reciprocal button (1/x) or typing in 1 then the divided by key then the frequency then the equals button.

Applying the wave equation

High E = 660 Hz
Example 1:
Sound waves in air travel at 330 m/s. What is the wavelength of a sound of 660 Hz (high E)?
Working out: v = f ×λ
so rearranging λ = v ÷ f which is 330 m/s ÷ 660 Hz which is 0.5 m

Example 2:

Radio waves travel at the speed of light. What is the wavelength of Newstalk ZB, which has a frequency of 89.4 MHz
Working out: f = 89.4 x 10^6 Hz. c = f × λ so λ = c ÷ f which is 3 x 10^8 m/s ÷ 89.4 x 10^6 Hz = 3.36 m
Note that yo need to convert MHz into standard form for this problem.
If you use negative index notation, and write Hz as per seconds (s to the power of -1) you would easily be able to see that units for this work out correctly. This isrecommended.

Note: Standard form
You are expected to write your answers in standard form. This note from Wikipedia explains a bit more about standard form for those of you unfamiliar with it. You may also need to know the more common metric multipliers, particularly k (kilo, 103), M (mega, 106), G (giga, 109) - for a full list go here. A detailed discussion of SI metric prefixes is here.

doppler.pngDoppler effect
When a source of waves is moving, it 'catches up' with the waves in front of it and leaves behind the waves behind it. This means that the wavelength of the waves preceding it is reduced, which increases the frequency to a stationary observer. This is illustrated in the diagram to the right, which shows waves given off by a police car travelling in the direction of the arrow (right). The waves to the right are bunched up, the ones to the left are spread out. The wdecrease in colour intensity simulates the decrease in volume as the wave energy spreads through a larger volume.
A ripple tank simulation is given here (requires java to run).
Doppler shift of sound: In sound waves, the doppler effect produces an increase in pitch for a sound source moving towards you. This is very noticeable with sources such as police sirens. The shift in frequency is known as a doppler shift.
The doppler effect also applies to EMR but is not as readily observable because few everyday objects move fast enough relative to the speed of light for the doppler shift to be discernible to human senses. However, police radar and laser speed guns rely on the doppler shift of reflected microwaves.
Sound waves: Doppler shift of sound waves has applications in sonar and measuring fluid velocity.
Astronomy: The Doppler effect also has applications in astronomy: we can work out the velocity of stellar objects relative to us by observing the doppler shift of known emission or absorbtion spectra from stars.
Other applications: Recent advances in laser and computer technology may make it possible to eavesdrop on quite distant buildings by measuring the tiny doppler shift of reflected laser light caused by sound vibrating the windowpanes.
The sound barrier: A boat travelling at very slow speeds would produce a ripple pattern like the one above. However, most boats exceed the speed of their own waves and produce the 'v' shaped wake more usually seen. This is analagous to the pattern of an object travelling greater than the speed of sound. The 'sonic boom' occurs when an object accelerates past the speed of sound and must pass through the compressions it generates.
Of course, the same situation cannot happen with light because nothing can go faster than the speed of light in a vacuum. However, particles can travel faster than the speed at which light propagates in a medium such as water, and this produces the characteristic blue radiation seen around reactors in pools of water; it is known as Cherenkov radiation.(see illustration furher down this page).

Section 2: Electromagnetic Radiation

Electromagnetic radiation is abbreviated as EMR. EMR consists of waves of electric and magnetic fields. They carry energy because the potential energy is constantly being transferred from the electric to the magnetic field.
EMR waves can be any size of wavelength. The symbol for wavelength is λ (lambda).

The range of EMR waves of different wavelengths is known as the electromagnetic spectrum. Different parts of it have different terms:

Source: Wikimedia Commons (click for original SVG)

Properties of electromagnetic radiation

EMR can travel through a vacuum (empty space), unlike sound. Its ability to travel through other substances depends on the substance. For instance, window glass is transparent to most EMR up to the near-ultraviolet, but relatively opaque to UV. The transparency of different substances to different wavelengths of EMR depends on the properties of the electrons in the subsance, and how their energy levels relate to the energy levels of the EMR.
EMR and energy: there is a relationship between the wavelength and energy of the EMR. Shorter wavelengths have more energy. The energy arrives in 'packets' called photons, which behave a bit like particles. It is the amount of energy per photon which is dependent on the wavelength or frequency (in fact, energy is directly proportional to frequency and is related by an equation E = hν., where h is a constant known as the Planck constant and v is the frequency expressed in radians per second). Infra-red is felt as heat because its energy levels corresponds to the energy of thermal vibrations in the atoms of your skin. Microwave ovens use microwave radiation with an energy similar to that on hydrogen-oxygen bonds in water; this is why the microwaves will heat the water in a cup of coffee, but not the cup itself.
When substances get hotter, the energy of the thermal vibrations increases and so they give off EMR waves with more and more energy, and so of shorter and shorter wavelength.

Refraction means the bending of waves when it travels from one medium to another e.g. with visible light: air to water, water to glass and so on.
Light travels at different speeds in different transparent substances. It is fastest in a vacuum, where it travels at 300,000 km per second
(or 3 x 108 m s-1). This is the fastest possible speed; NOTHING can go faster than this.
Light travels at about 200,000 km/s in glass. The ratio of the speed of light in a vacuum to that in a substance is called the refractive index. So the refractive index of glass is 300,000 km s-1/200,000 km s-1 = 1.5
Note that there are no units in this answer, because they cancel out. It is a dimensionless quantity.
It is the change of speed of the light that causes it to refract, or bend. Some of the waves are also reflected at the boundary; this is called partial reflection.

The amount of refraction depends on the speed of the waves in the medium. Light waves travel more slowly in glass than in water, so are refracted more:

diffraction.pngDiffraction: Waves, including EMR, will bend around a barrier as shown in the diagram on the right. This is due to the edge of the barrier acting like a point source of radiation.
The angle of diffraction depends on the wavelength - shorter wavelengths diffract at smaller angles.
A practical effect of this is that long-wave radio signals can be picked up more readily out of line of sight, because they are of sufficiently long wavelength that their diffraction angle causes them to follow the curvature of the Earth's surface; it can also diffract some distance over hills and so on so is less likely to suffer a 'shadow effect'. FM radio and TV is much shorter in wavelength and can be blocked by hills and so on; hilly cities like Wellington often require TV repeater stations for areas where hills block the main signal (FM radio can diffract over small hills but TV is shorter in wavelength).
click for original
click for original
Interference: When two point sources of waves are both giving of waves of the same frequency and wavelength very near each other, interference can occur. This happens because in some places the crests of two waves line up with each other all the time, as to the troughs. The superpose constructively, creating crests and troughs twice as high. In other places, the crests always line up with the troughs from the other source, and they always cancel each other out (destructive superposition). This creates an line where there are apparently no waves at all - the turquoise lines on the animated diagram to the left. This is called two point source interference. Because two narrow holes in a barrier can act like two point sources, it is fairly easy to create this. A famous experiment conducted by Thomas Young, scratching two thin lines with a razor on glass blackened with a candle, showed that light behaved as a wave.

Shadows: objects that block waves will produce a shadow. If the wave source is a 'point' source, the shadows will always be crisp. If it is not, the two sides of the light source will act in a similar way to two point sources and produce shadows in slightly different locations. In part of the shadow the entire light source will be obscured; this is called the umbra. In the penumbra some part of the light source is visible.
The relative size of the penumbra and umbra depends on the size of the light source, the distance from the light source to the shadow producing object and the distance from the object to the screen. This is why your shadow on the ground has crisp edges at your feet and more blurry edges at your head.

Because X-rays are essentially shadows of your bones or other tissue, it is desirable for the subject to be as close to the film as possible to make the shadows clear. It is also desirable to make the X-ray source as close to a point source as possible; in the early days of the technology this was difficult.
In a solar eclipse people in the umbra see the moon cover the entire of the sun. People located in the penumbra see only part of the sun obscured. By a rather remarkable coincidence, the apparent size of the Sun and Moon as seen from the Earth are nearly identical; with the fact that the Moon's orbit is slightly eliptical this means that occasionally the Moon is too far away to produce a complete umbra and a little bit of the Sun is visible right around the edge, in an 'annular' eclipse (this would be a region of the shadow called the antumbra). The similarity in apparent size between the Sun and Moon as seen from the Earth is truly amazing, but scientists so far have failed to come up with a convincing explanation other than coincidence. If there really were such a thing as alien visitors, this might be what they come to see - it is likely to be truly a rare event on a galactic scale!
Venus and Mercury are too far away relative to the Sun for us to see the umbra, so we see only the antumbra in an event called a transit. It was the transit of Mercury in 1769 that allowed Captain Cook to pinpoint the longitude of Mercury Bay, and thus produce an exact map of the rest of New Zealand.
A pinhole camera works on the principle that the hole is so small that all shadows are of the umbra only, producing a sharp image.

Cherenkov radiation (click for info)
Cherenkov radiation (click for info)
Section 3:Radioactivity

Introduction: Early researchers found that certain substances had the ability to cause photographic film to become exposed without light. This mysterious occurrence was thought to happen because of invisible ‘radiation’ from these substances. Substances which did this were ‘radioactive’; they were found to contain elements towards the end of the periodic table such as uranium, thorium, radium and polonium.
Some substances, e.g. doped zinc sulfide, glow in the presence of radiation. Radiation was also found to cause burns with sufficient exposure. People who experience these burns also developed more cancers (although this was not discovered until much later).
The radiation was discovered to fall into three groups:
  • Able to pass through a few cm of air, but stopped by paper. This was called alpha (α) radiation. This was also found to be positively charged. Alpha rays are now known to be helium nuclei.
  • Able to pass through several metres air, through a sheet of paper, but stopped by aluminium foil. This was called beta (β) radiation. It is now known to be electrons. It is negatively charged.
  • The third sort was able to pass through centimetres or more of concrete, and was neutrally charged. It is called gamma (γ) radiation. It is now known to be a form of electromagnetic radiation with a wavelength in the picometre range.
Normally, radiation is invisible. However, some types of radiation can cause a blue glow in water if it is travelling faster than the speed of light in water (Cherenkov radiation - click on photo for more information).

Decay paths
When radioactive elements decay, they can change into something else:
When they decay by alpha decay, they give off two protons and two neutrons. So their atomic number decreases by two and the mass number by four.
When they decay by beta decay, a neutron has changed into a proton, so the atomic number increases by one, and the mass number is unchanged.

We have symbols for writing elements:


The top number is called the mass number. It is the total number of protons and neutrons (given the symbol M). The bottom number is called the atomic number and is the number of protons; it is given the symbol Z. “C” is the symbol for the element carbon. This is often abbreviated to carbon 14 or C-14. I will do that here because of the difficulty of trying to superscript properly in the wikispace.

Nitrogen (element number 7): N-14 has 7 protons and 7 neutrons
Uranium (element number 92): U-238 has 92 protons and 146 neutrons; U-235 has 92 protons and 143 neutrons.
Notice that there are two different sorts of uranium. They are different isotopes of uranium. They are different because they have different numbers of neutrons (you can’t change the number of protons without changing the element symbol). Most elements have several isotopes. For example, there are three isotopes of carbon:
Carbon 12 has 6 protons and 6 neutrons, carbon 13 has 6 protons and 7 neutrons and carbon 14 has 6 protons and 8 neutrons .
Only carbon 14 is radioactive. The other two isotopes are stable isotopes, and carbon 14 is a radioisotope. Elements below number 88 have both stable and radioisotopes, but element 88 (radium) and above have only radioisotopes.
Carbon 14, being a radioisotope, decays, i.e. it is radioactive and changes into something else. C-14 decays by beta decay, so a neutron changes into a proton. We can write an equation for this process:

(sorry, this is proving difficult at the moment. Will try to fix in the next few days)

Notice that both the top line and the bottom line of the equation add up to the same on both sides of the arrow.

Radiation hazards
Only gamma radiation can penetrate tissue to any extent. Ionizing radiation causes damage to cells by creating reactive chemicals called free radicals in cell fluids. These can damage DNA or, in high concentrations, other cell structures such as cell membranes and organelles.
Alpha and beta radiation can still cause radiation sickness through exposure to fallout, where radioisotopes are incorporated into tissue. An example is iodine-131, which can become part of the thyroxine (hormone) molecule instead of normal iodine. Because it is inside the cell, the alpha and beta rays are able to ionize cell fluids and create free radicals. Strontium-90 is another example; it can replace calcium in bone cells.
X-rays are also ionizing and penetrating, so have similar hazards to radioactivity. This is why procedures which involve high levels of X-rays such as CAT scans need to be evaluated for the risk/benefit tradeoff.

Radiometric dating
Most people have heard of carbon dating. Carbon-14 is created constantly in the atmosphere by the action of solar radiation on nitrogen-14. It then gets incorporated into the carbon cycle via photosynthesis, so the amount of carbon-14 in living things is in equilibrium with the atmosphere. We have no reason to believe the amount 14-C in the atmosphere has varied significantly in the last 100,000 years; even if it had, the effect on carbon dates would actually be minimal.
Once an organism is dead, it is no longer in equilibrium with the atmosphere and the amount of 14-C halves every 5370 years by beta decay (changing it back to nitrogen-14). The amount of 14-C in anything that was once alive can therefore be compared to that in the present atmosphere (actually, that of 1945 because atmospheric nuclear testing has influenced the amount since then) and the age determined e.g. if it was 1/4 present, the sample would be about 11,000 years old.
Analysis is by gas chromatography and is very sensitive, but samples older than about 7 half-lives contain too little 14-C to be reliably detected and are too prone to contamination by modern carbon (a single modern pollen grain would significantly change the apparent age). Most geologists regard 14-C ages older than 35,000 years as being effectively unknown unless there is strong supporting evidence or particular rigour to prevent contamination.
Other radiometric isotopes are used. Any short lived isotope must be continuously created, usually in the atmosphere. Hydrogen-3 (tritium) is often used to measure groundwater transit times (half life 12 years; average transit time for groundwater feeding Lake Taupo is 70 years which is suited to this method). It doesn't work for fossil water millions of years old such as those common in Australia.
Rocks are commonly dated using isotopes with half-lives of billions of years. Some merthod must be used to determine the original amount of the isotope in the rock, e.g. through daughter products. For example, potassium argon dating relies on the fact that argon, being an inert gas, cannot be incorporated into crystalline chemical compounds (minerals). Any argon present in a potassic mineral must be formed by decay of potassium-40 (half life about 4 billion years). The amount of potassium 40 in the original sample can be determined, as it is a fixed proportion of the total potassium content. Argon can be extracted by heating the rock and its amount can be measured, thus the age determined.
All such ages require careful analysis; there are ways that non-radiogenic argon can be incorporated into some rocks, or some magmas may be contaminated with crystals of older rock from around the magma chamber. Anomalous dates are well known, e.g. Mt Ngauruhoe yields an improbable 250,000 year age when subjected to this technique, probably due to crustal contamination (Ngauruhoe is known on other evidence to be only a few thousand years old). Young-earth creationists make much of this, even supposing a 'conspiricay' about it. Geologists understand it well, and all radiometric ages are considered along with other age evidence. This is good science.
All long-lived isotopes used for dating must have been created by the supernova explosion, some 8 billion years ago, which created the elements heavier than iron present on Earth (our Solar System is condensed from the debris of this explosion). Thus the short-lived isotopes created in this event have mostly gone; very very long lived ones would be unsuitable and the remainder are present in significantly smaller amounts than in the primordial Earth (4 by ago). This limits the range of isotopes that can be used. It also means that most of these techniques are unsuited to geologically rather young materials (dates less than 1 million years are among the hardest to determine).
One technique using long lived but quite radioactive isotopes is fission track dating. Some minerals, notably zircon and apatite, contain significant uranium as an impurity. When the uranium undergoes alpha decay, the alpha particle damages the crystal structure along its path. If you cut the crystal in half and polish the surface, then lightly etch it with hydrofluoric acid, the tracks can easily be seen and counted with a microscope. To determine the amount of uranium, the remaining half is exposed to a high neutron flux in a reactor which causes all remaining uranium to decay. The ratio of fission tracks in the irradiated half to the other half determines the age.
Like all techniques, it isn't perfect. In particular, the fission tracks can 'heal themselves' over time, particularly if subject to heating (a phenomenon called annealing). This produces an anomalously young age. Tracks in glass around crystals are very prone to this. Fission track is useful for that very inconvenient gap between C-14 and K-40 (40,000 to 1,000,000 years) but many glass fission track ages for NZ volcanics were a little too quickly accepted. More careful work with zircons has seen these ages revised substantially upwards e.g. from abou 760,000 years for a prominent ignimbrite from the Mangakino Centre, to 1.1 million years.

Geiger Counter
This detects radiation by using a gas-filled tube (neon or similar). When ionizing radiation (alpha or beta) passes into it, it dislodges an electron from a gas atom. There are charged plates on either side of the gas, so the atom moves towards the negative plate and the electron to the positive one. The moving charges create a cascade of further charges as they collide with other atoms, eventually reaching the plates and creating a temporary electric current. this comes through as a 'click' on a loudspeaker, or some other detection method. Geiger counters are not such efficient detectors of gamma radiation as it can be too high in energy and pass right through the gas. (diagram coming when I have time)

Smoke detector
(coming when I have time, read the Wikpedia entry here)