IAL 7: Spectra

Don't Panic


  1. Thermodynamics
  2. Blackbody Radiation
  3. Wien's Law
  4. The Stefan-Boltzmann Law
  5. Line Spectra and Spectroscopy
  6. Star Spectra
  7. The Doppler Effect

  1. Thermodynamics

  2. To understand light spectra (previewed in the figure above: local link / general link: line_spectrum_iron.html), we have to review a bit of relevant thermodynamics.

    In brief, thermodynamics is the science of heat energy and temperature and their relation to relevant important variables of the macroscopic state of a system---these variables are the thermodynamic variables.

    Temperature is illustrated by the thermometers with Celsius temperature scale and the obsolete Fahrenheit temperature scale in the adjacent figure below (local link / general link: thermometer.html).

    thermodynamic variables include amount of heat energy, temperature, pressure, volume, density, entropy, matter phase, and, in general, chemical abundances.

    How heat energy determines the MICROSCOPIC state of a system is also part of statistical mechanics (the microscopic version of thermodynamics or the microscopic complement to classical thermodynamics)---but we will largely skirt that.

    We need to discuss briefly certain points of thermodynamics:

    1. Thermodynamic Equilibrium:

      Thermodynamic equilibrium is the state when the thermodynamic variables are unchanging in time.

      Thermodynamic equilibrium is a timeless and lifeless state at the macro-level. A body in thermodynamic equilibrium does NOT change color, size, phase, or chemical composition. It just stays as it is.

      Microscopically, change continues to happen.

        Atoms and molecules move around.

        In gases and fluids, they can translate and rotate and have internal motions. In solids, they can't translate or rotate usually, but they can oscillate and have internal motions.

        All kinds of microscopic processes can happen too: e.g., chemical reactions and transition.

        But the reverse processes have to balance the forward processes. There is detailed balance in physics jargon.

      Temperature, among other things, is a measure of thermodynamic equilibrium. An unchanging system all at one temperature is in overall thermodynamic equilibrium.

      Thermodynamic equilibrium is easy to analyze and systems in thermodynamic equilibrium are common, and so thermodynamic equilibrium is very important.

      Absolutely vital is that many systems evolve slowly enough in time that they are in thermodynamic equilibrium to some approximation at every instant.

      Such an evolution is a quasistatic process.

      Quasistatic processes are common and allow us to stretch the concept of thermodynamic equilibrium to large realms of reality.

      Quasistatic processes are also useful in theoretical developments and understanding.

      Of course, there are many systems NOT in thermodynamic equilibrium and NOT quasistatic. Any system with internal variations in temperature and/or energy flows is NOT in thermodynamic equilibrium and NOT quasistatic.

      Analyzing such complex systems is hard, but, of course, it is done, often by breaking a system into component subsystems that are in thermodynamic equilibrium or are quasistatic. For example, the Sun-space-biosphere (SSB) system which is explicated in the figure below (local link / general link: disequilibrium_life.html).

    2. Macroscopic-Scale Motions:

      A naive first thought is that macroscopic scale motions as outside of thermodynamics, but actually they must be considered inside thermodynamics.

      Macroscopic motions affect the thermodynamic variables cited above and are affected by them: e.g., a macroscopic squeezing of a sample can increase its pressure and pressure can cause macroscopic motion (e.g., in heat engines and hydraulics).

    3. Heat Energy:

      What is heat energy?

      Heat energy (or just heat or properly internal energy) is statistically distributed microscopic energy of various forms.

      A short list of heat energy forms follows:

      1. Microscopic kinetic energy (i.e., the energy of microscopic motions). The animation in the figure below (local link / general link: gas_animation.html) illustrates this kind of heat energy.

      2. Microscopic potential energy (AKA field energy) which is the energy of position in microscopic fields of force: these being the electric field, magnetic field, and the strong nuclear force field of force.

        Microscopic bonding energies of all kinds (e.g., ionization energies, chemical bond energies, and nuclear bond energies) and microscopic interation energies are all field energies.

      3. Thermal radiation: Thermal radiation and its very important special case is called blackbody radiation are explicated below in section Blackbody Radiation.

        Note that thermal radiation is often loosely used as a synonym for blackbody radiation---which is OK as long as you know what you mean.

      4. Other forms we won't go into here: e.g., atomic nucleus and neutrino energies.

    4. Extensive Quantities and Intensive Quantities:

      In thermodynamics, there are two categories of quantities (i.e., thermodynamic variables): extensive quantities and intensive quantities.

      An extensive quantity is proportional to the mass or volume or count of entities or some other measrure of the size of a system.

      Mass and volume are themselves extensive quantities. Heat energy is another extensive quantity: one just adds up bits of heat to get the total amount in a sample.

      Intensive quantities do NOT depend on the size of a system in any sense (i.e., they are independent of the scale of the system) and are often ratios.

      For example, density (which is the ratio of mass/volume) is an intensive quantity. A system of any size can have any density.

      Temperature (which we discuss in the subsection just below) is another intensive quantity, but it is NOT a ratio in obvious sense.

    5. Temperature in Thermodynamics:

      Temperature is actually a darned hard thing to define completely in its most fundamental modern sense without knowing statistical mechanics.

      A stab at an incomplete modern fundamental definition is as follows:

        Temperature is parameter that controls the distribution of particles among microscopic states: which are usually called energy levels.

        It is essentially a sort of microscopic average energy, but by ancient convention does NOT have the units of energy.

        Temperature was used in less fundamental ways before the modern fundamental definition was established.

        Originally, temperature may have been NO better defined that what one reads off a thermometer---but yours truly does NOT know the evolution of the meaning of the term temperature.

      The figure below (local link / general link: maxwell_boltzmann_distribution.html) explicates how temperature controls the distribution of particles among energy levels in the special case of the Maxwell-Boltzmann distribution for an ideal gas.

      What else is

      1. At the macroscopic level, temperature is, among other things, the measure of the thermodynamic equilibrium as we have discussed above.

        For example, if a system is all at one temperature, it is all in thermodynamic equilibrium with itself---in the temperature thermodynamic variable sense though NOT necessarily in all thermodynamic variables (e.g., pressure).

      2. Temperature is also a measure of the mean kinetic energy of microscopic particles which actually is consequence of it determining the Maxwell-Boltzmann distribution to recapitulate from the explication in the figure above (local link / general link: maxwell_boltzmann_distribution.html).

      3. And of course, temperature a quantitative measure of our qualitative sense of hot and cold.

      Recall from IAL 1: Scientific Notation, Units, Math, Angles, Motion, Orbits that in this course we usually only use the thermodynamic temperature scale or, as it is often called, the Kelvin temperature scale.

      The unit of the Kelvin temperature scale is the degree kelvin (equal in size to the Celsius degree).

            Absolute zero is T_K = 0 kelvin or T_C = -273.15 C. 

        Question: We put a cup of hot coffee and a vat of hot water in thermal contact (i.e., we allow heat transfer proceses to operate) and isolate them from the rest of the world and NOTHING happens to either.

        1. The cup and vat had different temperatures (i.e., different states of thermodynamic equilibrium), but then heat energy flowed from COLD TO HOT and the two came into a mutual state of thermodynamic equilibrium.

        2. The cup and vat had different temperatures (i.e., different states of thermodynamic equilibrium), but then heat energy flowed from HOT TO COLD and the two came into a mutual state of thermodynamic equilibrium.

        3. The cup and vat had the same temperature originally (i.e., were in thermodynamic equilibrium with each other in a limited sense before they were put in contact) and no net heat flows occurred (when they were put in thermal contact). Microscopic heat flows that average to zero do occur.

        Answer 3 is right.

        There are no spontaneous heat flows at the macroscopic level between objects of the same temperature: they are in thermodynamic equilibrium with respect to each other.

      Absolute zero is the state where all microscopic energy that can be removed from a system has been removed.

      Note quantum mechanics dictates that there is an irremovable amount of energy, the zero-point energy.

      So there is a coldest: absolute zero.

      However, there are negative temperatures on the Kelvin scale. This remarkable fact is explicated in the figure below (local link / general link: 1919_solar_eclipse_negative_thermo.html).

    6. Thermodynamics: The Practical Science:

      Thermodynamics has always been an eminently practical science.

      It is the science needed for heat engines and refrigerators. See the figure below (local link / general link: heat_engine_schematic.html) illustrating a schematic heat engine.

      The figure below (
      local link / general link: internal_combustion_engine.html) illustrates how the schematic heat engine is realized by the internal combustion engine (ICE).

  3. Blackbody Radiation

  4. Thermal radiation, blackbody radiation and the blackbody spectra are explicated in the figure below (local link / general link: blackbody_spectra.html).

    applet in the figure below (local link / general link: naap_blackbody.html) dynamically illustrates the blackbody spectrum.

    Some examples of
    blackbody radiators, approximate ones, and variations from them are discussed below:

    1. Incandescent Light Bulb Filaments:

      The filament of an incandescent light bulb. See the incandescent light bulb filament in the figure below (local link / general link: light_incandescent_filament.html).

    2. Candle Flames:

      Is a candle flame with a temperature of about 2000 K a blackbody radiator or is the combusting gas too dilute? In fact, a candle flame is too dilute to be an exact blackbody radiator though its spectrum is partially like a blackbody spectrum. See Wikipedia: Flame: Color.

    3. Stove Grills:

      A stove grill that is red-hot. It's actual temperature must be much lower than 1000 K---just guessing. If the guess is right, its blackbody-spectrum peak is at ∼ 3 μm (from Wien's law: see below section Wien's Law) which is in the IR (infrared).

    4. The Human Body:

      The human body (illustrated abundantly in the figure below (local link / general link: beach_bondi.html) has fiducial temperature 310 K (see Wikipedia: Human body temperature) and, therefore has its blackbody-spectrum peak at ∼ 10 μm (from Wien's law: see below) which is well into IR (infrared).

    5. Stars:

      Stars, including the Sun, approximate blackbody radiators which is a key reason for studying blackbody radiators here.

    6. Hohlraums:

      A useful experimental setup that is a near-perfect blackbody radiator is a completely closed oven---which in ancient physics jargon is called a hohlraum.

      The walls of the oven are held to uniform temperature and emit pure blackbody radiation at that uniform temperature.

      The walls also absorb and reflect that blackbody radiation, but all proceses cancel out and a detailed balance is maintained with electromagnetic radiation (EMR) inside the hohlraum in thermodynamic equilibrium with the walls.

      The EMR inside the hohlraum is near perfect blackbody radiation.

      A small, negligibly perturbing aperture allows one to study the radiation field.

      The blackbody spectrum obtained is more perfectly blackbody-like than almost an in nature. The cosmic microwave background (CMB) (which we discuss in section Wien's Law below) is one of nature's most near-perfect blackbody emitters.

    7. Purcell's Blackbody Box:

      Actually, any small aperture to an internally unilluminated closed space at human-scale temperatures is a pretty good blackbody in the sense of NOT reflecting much though usually NOT in being blackbody radiator radiating a blackbody spectrum.

      A useful toy that illustrates this is the Purcell's blackbody box or Purcell's hohlraum: see the figure below (local link / general link: purcell_hohlraum.html).

      Purcell's hohlraum is just box with a small hole for viewing the interior.

      Very little visible light can be reflected out of the viewing hole if small enough.

      No matter what the interior color of a Purcell's holhraum, the hole looks very, very black.

      The hole is a very perfect non-reflecter: i.e., a blackbody.

      A blackbody spectrum with room temperature is being emitted from the hole, but that spectrum peaks well into the infrared, and so we can't see it.

    8. Vantablack:

      Nowadays, we can make very black materials which are also close to being blackbodies as REFLECTERS, but NOT usually as emitters. As an illustration of a very black material, see vantablack in the figure below (local link / general link: vantablack.html).

    9. Mixtures of Blackbody Spectra:

      Dense bodies with varying temperature are NOT blackbody radiators, but have spectra that are mixtures of the blackbody spectra at different temperatures.

      Mixtures blackbody radiation would be thermal radiation---here NOT used as a synonym for blackbody radiation.

      Of course, there are radiators that are NOT at all like blackbody radiators: e.g., dilute gases as we will discuss below.

    10. Blackbody Radiation Videos:

      As a recapitulation of this section, see Blackbody radiation videos below (local link / general link: blackbody_videos.html).


  5. Wien's Law

  6. There are two basic formulae that follow immediately from the blackbody spectrum law (AKA Planck's law): Wien's law (which we take up here) and the Stefan-Boltzmann law (which we take up in the next section The Stefan-Boltzmann Law).

    Wien's law (AKA Wien's displacement law) determines intensity maximum (in units of energy/(area*steradian*time*wavelength)) of a blackbody spectrum.

    1. Wien's Law Explicated:

      Wien's law is explicated in the figure below below (local link / general link: wien_law.html).

    2. Examples of the Use of Wien's law:

      Examples of the use of Wien's law are given in the table below.

       Table:  Examples of the Use of Wien's Law
       Object         Approx. T (K)   Approx. λ_Max     Comment
       hot star            40000         0.075          far in UV
       Solar photosphere    5778         0.5015         the peak is 
                                                        near the blue end of green light,
                                                        but the mixture of wavelengths
                                                        is dominated by yellow or white. 
       human body            310        10              in IR
        -so we-all
        thermally radiate 
        in the IR, but
        reflect mainly
        in the visible.
       Pluto's surface        37        80              far in IR for blackbody radiation,
                                                          of course, we see Pluto by 
                                                          reflected sunlight in the
                                                          visible. The images of Pluto
                                                          by the New Horizons spacecraft
                                                          are of relected light.
                                                          See New Horizons Pluto images.

      From Wien's law you can determine the wavelength of maximum of EMR emission for any body at a given temperature---insofar as that body approximates a blackbody.

      Wien's law can be inverted, and thus if you know the shape of spectrum that approximates a blackbody, you can estimate the temperature of the emitting surface.

      This is a crude, but very useful, way of finding star surface temperatures.

    3. The Cosmic Microwave Background Radiation (CMB):

      The background EMR field of the question just above in subsection Examples of the Use of Wien's law is called the cosmic microwave background radiation (CMB).

      It is a relic of the recombination era of the universe which happened about 400,000 years after the Big Bang.

      The CMB, in fact, is a nearly perfect blackbody spectrum---one of the most perfect in nature.

      See the CMB in the figure below (local link / general link: cmb.html).

      The discovery in 1965 of the CMB was the crucial evidence that convinced most people that something like a Big Bang had happened. The discovery is discussed in IAL 30: Cosmology: The Cosmic Microwave Background (CMB).

  7. The Stefan-Boltzmann Law

  8. Just for completeness, we should give the Stefan-Boltzmann law.

    This law gives the total power per unit area (i.e., radiant flux (AKA flux)) emitted by a blackbody radiator.

    This is the power per unit area summed/integrated over all wavelength.

    For us, the importance of the Stefan-Boltzmann law is that it shows that the power of a radiator increases strongly with increasing temperature.

    The Stefan-Boltzmann law is described in the figure below (local link / general link: stefan_boltzmann_law_logarithmic.html).

  9. Line Spectra and Spectroscopy

  10. Dense materials have effectively a continuum of emission and absorption channels with wavelength, and so they can emit or absorb a wavelength continuum of EMR which in the case that the material is at one temperature is a blackbody spectrum.

    But atoms, molecules, and ions in dilute gases do NOT have such strong continuum of emission and absorption channels. They have some, but we won't worry about them here.

    Such dilute gases tend to have their strongest emission/absorption in a discrete set of narrow wavelength bands that are called spectral lines or transition lines or just lines for short.

    Line spectra are usually created by diffraction gratings. How diffraction gratings work is explicated in the figure below (local link / general link: diffraction_grating.html).

    For an example of a
    line spectrum, see the figure below (local link / general link: line_spectrum_iron.html).

    The study of
    line spectra is called spectroscopy.

    Why are there line spectra what kinds are there, and what can we do with them? We explicate in the subsections below.

    1. Quantum Mechanics and Line Spectra:

      Quantum mechanics explains why atoms, molecules, and ions have spectral lines.

      An atomic transitions/molecular transition is a change in the internal energy state of the atoms, molecules, or ions.

      These energy states have only certain discrete energy values: they are QUANTIZED.

      To conserve energy, energy must be emitted or absorbed during transition.

      The energy change can only come in set of quantized values depending on the quantized states.

      Emitting or absorbing EMR in photons is one possible way of conserving energy.

      Thus, emitted photons have quantized energy values which give the spectral lines.

      A longer explication is given in the figure below (local link / general link: atom_diagram_abstract.html).

    2. Emission Line Spectra:

      If you just have a hot, dilute gas then usually you will see an emission line spectrum from photons from the spectral lines of atoms, molecules, and/or ions.

      The line spectra of a species is nearly unique and has become the most important identifier of that species in modern science.

      The study of line spectra is spectroscopy.

      Spectroscopy is the most important of all chemical analysis tools---it tells us what matter is made of.

      It is vastly easier than doing chemical reactions for chemical analysis.

      And you don't have to have the matter in your hand---you just need line spectrum from the matter---either an emission line spectrum or an absorption line spectrum (see below).

      Spectroscopy tells us what observable universe is made of---without leaving Earth.

      A continuous spectrum and a emission line spectrum are compared in the figure below.

      In many cases, just by looking at the line spectrum from a gas many of the constituent atoms, molecules, and/or ions can be identified BY EYE by experienced spectroscopists.

        I'm sort of a spectroscopist myself---but evidently NOT a good one since I can't do this---except in special cases.

      A line spectrum can be created and studied using a spectroscope (see the figure below: local link / general link: spectroscope.html) which is just a device that disperses light into a spectrum.

      But for an line spectrum you don't see a long band of colors gradually changing; you see just isolated strips (i.e., lines) of colors surrounded by relative darkness.

    3. Examples of Emission Line Spectra:

      Some example atomic line spectra and some star absorption line spectra are shown in the figure below (local link / general link: nasa_spectra.html).

      We explain absorption line spectra in section Star Spectra below.

      A recapitulation of the explanation of the formation of emission line spectra is given in Emission spectrum of hydrogen | 0:57 in Spectroscopy videos below (local link / general link: spectroscopy_videos.html).


    4. Other Things to Do with Spectroscopy:

      As well as identifying the atoms, molecules, and/or ions, one can also usually learn something about their abundances, and the temperature and density of a gas from spectroscopy plus modeling.

        Also one can determine the source's velocity relative to the observer along the line of sight. This makes use of the Doppler effect which is discussed below in the section The Doppler Effect.

      To reiterate: It is true to say that spectroscopy is the most important chemical analysis technique of all.

      You do NOT need a sample of a substance in your hand. You just need light from a hot low-density gas source containing the substance. The light could be from all across the observable universe.

      The ability to chemically analyze without having a sample in hand was NOT anticipated historically as discussed in the figure below (local link / general link: auguste_comte.html).

  11. Star Spectra

  12. What kind of spectra do we get from stars (e.g., the Sun)?

    We answer in a few subsections below:

    1. In the Interior of a Star:

      The EMR in the deep interior of a star is forced by high local opacity to be in thermodynamic equilibrium with its local environment: i.e., it has a blackbody spectrum with a temperature equal to that of the local matter.

      The interior is very hot with matter with temperatures typically rising from tens of thousands of degrees at the photosphere and reaching of tens of millions of degrees in the center. So typically in the deeper interior, the EMR's blackbody spectrum has a maximum in or near the X-ray band (fiducial range 0.1--100 Å) (HRW-802). Recall Wien's law λ_max = 2.8977729(17) Å*K/(T/10**7).

      But EMR from the deep interior does NOT escape the star. The photons that are emitted are absorbed after a short distance by matter.

      As discussed in IAL 6: Light and Electromagnetic Radiation (EMR) one can picture the EMR as photons on a random walk from the interior to the outside (see the figure below: local link / general link: photon_escape.html). This is an important example of heat energy flowing from hot to cold.

      In a random walk, photons are emitted in random directions from matter, travel some distance often scattering off atoms or free electrons, and then are absorbed.

      Their energy is then re-emitted as other photons, but at temperature corresponding to the matter where they are re-emitted from.

      The temperature, density, and opaqueness of a star decrease going outward. This gives a bias for longer flights in the outward direction. Near the surface the photons come from relatively low temperatures compared to the interior.

    2. The Stellar Photosphere:

      As the photons random walk out from the interior of a star, finally there is layer where the density is so low that outward going photons can escape to infinity at least about half the time.

      We call this layer the photosphere. See the figure above.

      The photosphere is the layer from which we see most EMR coming from the star.

      The photosphere often called the surface of the star.

      But, in fact, stars have no definite surface. Their density decreases going outward and probably becomes negligibly small at some point, but without a sharp cut-off.

      Many stars are probably like the Sun whose atmosphere extends into a solar wind where matter is blowing off the Sun. This wind extends outward until it merges with the interstellar medium (ISM).

      The photosphere is layer NOT exactly at a single temperature.

      Thus you will get a continuous spectrum from the photosphere that is a mixture of blackbody spectra at slightly different temperatures.

      Nevertheless, you can often fit the photosphere spectrum by a blackbody spectrum at a single temperature to high accuracy.

    3. Above the Stellar Photosphere is the Stellar Atmosphere:

      Although the photons can escape at most wavelengths from the photosphere, the lines of atoms, molecules, and/or ions are particularly strong absorbers even when continuum absorption has grown weak because of low density.

      So above the photosphere in what is called the stellar atmosphere, the lines will absorb some of the continuous spectrum in the narrow wavelength bands corresponding to the lines.

      They absorb because the atoms, etc., are colder than the EMR from the photosphere.

      This line-absorbed EMR is reprocessed into some other form of energy which eventually escapes the star are as EMR, but mostly NOT in the wavelength bands were it was absorbed.

      The absorption by the lines creates an absorption line spectrum: a bright continuous spectrum with superimposed dark absorption lines.

      The figure below (local link / general link: spectrum_formation.html) illustrates how absorption line spectra are formed.

      The figure below shows a cartoon of an
      absorption line spectrum in intensity representation.

      A recapitulation of the explanation of the formation of absorption line spectra is given in the video Spectrum of the Stars | 0:54 in Spectroscopy videos below (local link / general link: spectroscopy_videos.html).


    4. The Solar Spectrum:

      An example of an absorption line spectrum is our old friend the solar spectrum.

      Let's first look at solar spectrum in image represention (which one gets directly from dispersion by diffraction grating) in the two figures below (local link / general link: solar_spectrum_image.html; local link / general link: fraunhofer_lines.html).

      In the figure below (
      local link / general link: solar_spectrum_graph_2.html) is a graph of the solar spectrum in flux representation. It is a log-log plot with a wavelength scale too coarse to show individual absorption lines.

  13. The Doppler Effect

  14. The Doppler effect (previewed in the animation in the adjacent figure: local link / general link: doppler_effect_siren_animation.html) is the shift in frequency/wavelength of a wave phenomenon from a reference frequency/wavelength and that shift depends on the motion of an observer and/or source of the wave phenomenon.

    The Doppler effect occurs for all wave phenomenon. Here we will only consider two really important cases: (1) the case of mechanical waves in a medium in the classical limit (i.e., when relativistic effects are negligible) and (2) the case of electromagnetic radiation (EMR) in the extreme limit where the EMR is in vacuum moving at the vacuum light speed c = 2.99792458*10**8 m/s ≅ 3*10**8 m/s =3*10**5 km/s ≅ 1 ft/ns.

    Hereafter, for brevity, we will usually just refer to the case of mechanical waves and the case of EMR.

    The Doppler effect is somewhat similar in the two cases, but the detailed behavior and the formulae are different.

    Now the natural reference frequency for the Doppler effect is the one that makes the analysis simplest.

    For mechanical waves (with the in the classical limit (which is all we'll consider here for simplicity), the natural reference frequency is, depending on the case, either of:

    1. The frequency of the wave phenomenon in the medium reference frame (i.e., the reference frame in which the observer is at rest with respect to the medium).
    2. The fixed emission frequency for a source of wave phenomenon: e.g., a siren.

    For EMR in the vacuum limit (which is all we'll consider here for simplicity), the natural reference frequency is the frequency of the emission of the source of the EMR.

    1. Doppler Effect Intro:

      The Doppler effect was first discovered by Austrian Christian Doppler (1803--1853) in 1842 for light. The application to sound came only a little later in about 1845.

      The Doppler effect for sound is, in fact, an everyday-life phenomenon.

      Pitch is the human psychoacoustical perception of sound frequency plus other sound features to a lesser degree.

      We notice that the pitch of a siren or aircraft changes noticeably as those pass you---from high to low---and so we notice the Doppler effect.

      The Doppler effect for sound is also used by bats---see the figure below (local link / general link: doppler_effect_bat.html).

      The Doppler effect for electromagnetic radiation turns up in everyday life with police radar guns which are used to judge relative speeds and catch speeders.

    2. Understanding of the Doppler Effect for Mechanical Waves a Medium in the Classical Limit:

      Understanding the Doppler effect for mechanical waves (i.e., for where there is a medium: e.g., sound waves and waves on a string) in the classical limit is easy qualitatively and NOT so hard quantitatively. An explication is given in the figure below (local link / general link: wave_propagation.html).

      The 3 figures below (
      local link / general link: doppler_effect_siren_animation.html; local link / general link: doppler_effect_spherical_waves.html; local link / general link: doppler_effect_sonic.html) further illustrate how the Doppler effect arises for mechanical wave in the classical limit---it's really very easy to understand qualitatively.

    3. The Doppler Effect for Electromagnetic Radiation:

      We explicate the Doppler effect for electromagnetic radiation (EMR) in vacuum in the figure below (local link / general link: doppler_effect_relativistic.html).

    4. The Doppler Effect in Astronomy:

      Now for the Doppler effect in astronomy.

        Question: The Doppler effect in astronomy is most useful for:

        1. Continuous spectra since you DO NOT know directly the shape of emitted spectrum if it has been Doppler shifted.

        2. Continuous spectra since you DO know directly the shape of emitted spectrum if it has been Doppler shifted.

        3. Line spectra since you know the position of the emitted spectrum lines since those are the positions one determines in the laboratory. In fact, since one can measure lab and astronomically-observed line positions very exactly, one can determine the relative line-of-sight velocity (i.e., relative radial velocity) to an astro-body to very high accuracy often.

        Answer 3 is right.

      You CANNOT know the shift of an observed continuous spectrum, unless you know what the emitted spectrum was like in its own rest frame and usually you do NOT know that until after you have determined the relative velocity.

      Note continuous spectra have an infinite range of behavior. So you CANNOT just try a finite set of articially shifted continuous spectra to get a fit an observed data. Note also continuous spectra are generally NOT pure blackbody spectra, and even if you knew one was a pure blackbody spectrum, you would NOT in general know the source's temperature. Note finally that even if you knew the intrinsic continuous spectrum of particular astro-body, that continuous spectrum can be modified by transmission through the interstellar medium (ISM) in a generally unknown way.

      The upshot is that continuous spectra are usually NOT too useful in determining radial velocities of astro-bodies.

      On the other hand, making use of line spectra to determine radial velocities is very easy as explicated illustrated in the figure below (local link / general link: doppler_effect_line_spectra.html).

    5. The Cosmological Redshift and the Gravitational Redshift:

      There are two similar wavelength shifting effects, that are often called Doppler shifts, that turn up in astronomy:

      1. The cosmological redshift which is discussed in IAL 30: Cosmology.

      2. The gravitational redshift which is discussed in IAL 25: Black Holes. A negative gravitational redshift is a gravitational blueshift.

      Some---like yours truly---consider it a mistake to call these effects the Doppler effect. Others are more relaxed about the use of the expression Doppler effect and say both those wavelength shifts are a Doppler effect.

      A comparison of the Doppler effect and the cosmological redshift is given in the figure below (local link / general link: cosmological_redshift_doppler_shift.html).