Earth and Space Science 2.7 (91193): Demonstrate understanding of physical principles related to the Earth System

External, 4 credits
Achievement
Achievement with Merit
Achievement with Excellence
Demonstrate understanding of physical principles related to the Earth System.
Demonstrate in-depth understanding of physical principles related to the Earth System.
Demonstrate comprehensive understanding of physical principles related to the Earth System.
1. Achievement criteria:
  • Demonstrate understanding involves describing physical principles related to the Earth System.
  • Demonstrate in-depth understanding involves explaining physical principles in terms of the Earth System.
  • Demonstrate comprehensive understanding involves linking physical principles to the Earth System.

Physical principles will be selected from:
  • source (solar and terrestrial) and transport of heat by radiation, convection and conduction
  • transmission, reflection, absorption, and scattering of visible and/or infra-red radiation.

The Earth System contains the hydrosphere, atmosphere, geosphere, and/or biosphere


Resources:



Physics of heat - write in workbook (based on old School Cert content) - SHC students only Answers (note - 6 Mb file on Google Drive, private to SHC)

I am moving in some material from the old L3 Science/Physics standard; some links have been lost. I will rebuild this as I have time.
To get the full material go to:
http://ncealevel3science.wikispaces.com/Physics



Section 1: Waves - an introduction

swells.png
Ocean swells near Lyttleton
Waves consist of a regular cycle between two forms of energy. For instance, in sound waves the energy changes between elastic potential energy and kinetic energy. Waves in the ocean oscillate beween gravitational potential energy and kinetic energy, and 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:
wave.png
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:
longitudinal.png
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:
equation.png
where
  • 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

hghe.JPG
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 (which is difficult for me to do here on wikispaces at the moment because I don't seem to be able to supescript or subscript). 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, 10^3), M (mega, 10^6), G (giga, 10^9) - 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 EMR 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 or sound waves.
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.
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.
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 . Of course, the same situation cannot happen with light because nothing can go faster than the speed of light. But particles can travel faster than the speed of light 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:

EMspectrum.png
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:
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.

refraction_wave_model.png
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:
plane_refraction.png

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.
shadow.png


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.