Physics 101 - Astronomy - Spring 2019

Class notes for day , Jan. 31, 2019

 We had severe weather this morning and so I postponed the exam until next week. For the small number of students who could make it to class, I began some material that comes after the first exam. Much of this relied on demonstrations in class, so if you didn't make it, take a look at ch. 5 in the textbook.

Instead of a Powerpoint, we will use this web page and in-class demonstrations to illustrate ideas from Ch. 5.

Ch. 5 - First part - WAVES

I will use simulations along with demonstrations in front of the class to start discussing Ch. 5 on Radiation and Spectra. These simulations will be run using Internet Explorer in the classroom; your browser may not be set up to work with these.

To get the idea of waves, I used this simulation page from Dan Russell (who was a student at Bradley Univ., where I taught for a few years). He has given permission to use these in our classes.

Two types of waves are shown here; the middle simulation is a longitudinal pulse, like a sound wave, and the bottom one is a transverse pulse:

http://www.acs.psu.edu/drussell/Demos/waves-intro/waves-intro.html

To illustrate frequency, wavelength, and velocity of periodic waves, I used several simulations. You might want to open these links in a separate window of your browser, then follow the textual description that I give on this page. These are meant to expand on the text, you don't need to follow all the detail that you see in these simulations.

If you start a pulse traveling along a rope, cord, or Slinky spring, like I did in class, you see that it travels at a velocity, and it might be reflected from a boundary, as in this simulation of single traveling pulses (just look at the pulses, don't worry about the explanation, it's too detailed):

http://www.acs.psu.edu/drussell/Demos/reflect/reflect.html 

In a cord, a force, called tension, is needed to get the wave to move along. Remembering Newton's Second Law, in order to get a mass (the string) to move, there must be a force. A slack string would not be able to have waves on it. Reflections may invert a pulse, or not, depending on the properties of the place (object, surface, etc) where the reflection occurs, as seen in the simulation.

Waves are often classified into two types of waves: transverse and longitudinal. The difference is shown in this simulation:

http://www.acs.psu.edu/drussell/Demos/waves/wavemotion.html

In the simulation below, if you click on the link, you can click on PLAY to see a simulation of a transverse wave (the red curve on top) and a longitudinal wave (the purple band on the bottom). To replay the simulation, click on RESET, then again on PLAY. Notice how the colored dots (black, green, and blue) move for the two types of wave. Examples of transverse waves are waves on strings and electromagnetic waves. An example of longitudinal waves is sound in air (or liquids) and some types of sound in solids.

http://webphysics.davidson.edu/physlet_resources/bu_semester1/c20_trans_long.html 

Waves have a wave speed, or wave velocity (we use v to indicate Velocity) and it may vary for different waves. In the following simulation, the crests of the wave on top travel faster, so it has the higher velocity. This might be a result of having a more massive (or thicker) string for the slower wave on the bottom (the purple one). The "medium" of the wave is the string (for waves on a string) or air (for sound) or water (for ocean waves) or space itself (for electromagnetic waves).

http://webphysics.davidson.edu/physlet_resources/bu_semester1/c20_wave_speed.html 

Waves also have wavelength and period. In this simulation, don't worry about the comment on "phase" but look at the distance between two adjacent crests. This is the wavelength, and we use Greek letter lambda l (Greek for L) to stand for wavelength (it is a Length, after all, but someone used L for another concept, so we use lambda l for wavelength). The blue curve that appears on the bottom when you click on PLAY is a graph of the motion of the blue dot in the wave on top. Notice that the blue dot repeats its motion after an interval of time, called the PERIOD. The period (denoted by T for Time) is the inverse of frequency (we use f to denote frequency): T = 1/f
I gave several examples in class: for example if your heart beats two times per second, the frequency is 2 Hz and the period in 1/2 s. Hz stands for Hertz, or Cycles Per Second. Or if a tuned bar vibrates 440 times per second, the frequency is 440 Hz (which is the musical note A), and the period is (1/440) s. The amplitude of the wave is the maximum distance that the individual points of the medium travel away from their original position. For example, in the top part of the figure, it is the "height" of the crest above the horizontal line. The vertical distance between crest and trough is twice the amplitude. The words "crest" and "trough" here are used in the sense of "top of the hill" and "bottom of the valley, or ditch."

http://webphysics.davidson.edu/physlet_resources/bu_semester1/c20_wavelength_period.html 

Frequency, wavelength, and velocity are related by an equation:  l = v/f This equation can be derived from the idea that the crest of the wave travels to the position of the next crest of the wave (it travels one wavelength l ) during a time interval of one period T. Since it goes at velocity v, the distance l = vT. (This comes from the fact that distance = velocity times time.) Then since T = 1/f we can make a substitution l = v/f = vT.
This simulation shows two waves that have the same velocity v, but the lower one has higher frequency, and hence it also has a shorter (smaller) wavelength. This is consistent with the equation. If f is larger, then v/f is smaller (if v is unchanged), which means l is smaller.

http://webphysics.davidson.edu/physlet_resources/bu_semester1/c20_wave_fvl.html 

Ripple Tank is a demonstration of waves in two dimensions, like the waves on the surface of a pond. This demo can show diffraction from a single slit, or interference from two slits. These are shown if you choose from the drop-down menus.

http://www.falstad.com/ripple/ 

Sound intensity vs. radius. This shows how waves get weaker as they travel out from a small source, since the waves spreads out over more "area".

http://webphysics.davidson.edu/physlet_resources/bu_semester1/c20_sound_intensity.html 

The Doppler effect occurs when a source of sound is moving. An example is the change in frequency when a fast vehicle passes by you, like an ambulance:

http://www.walter-fendt.de/html5/phen/dopplereffect_en.htm

Doppler effect - this shows the effect of variable speed:

http://www.acs.psu.edu/drussell/Demos/doppler/doppler.html

Here is another simulation where we can adjust the speed (see bottom of this web page)

http://webphysics.davidson.edu/Applets/Applets.html  (Unfortunately, during class this crashed the computer and I used the blackboard to do some calculations with the wave equation. I'll try again Thursday.)

A bigger version can be produced with the Falstad simulations (if you can get this to work)

http://www.falstad.com/ripple/

and I demonstrated this with a whistle attached to a cord and swung around my head. Students in the audience heard a higher pitch as the whistle moved toward them and a lower pitch as it moved away from them.

Ch. 5 - Second part - FIELDS and ELECTROMAGNETIC WAVES

The following simulations are meant to illustration the idea of electric and magnetic FIELDS, then motivate the idea of electromagnetic fields. If you missed my explanations of these, it will be hard to get much from them. They are just meant to give an impression of how these fields can give rise to waves. I showed how iron filings can be used to see the magnetic field pattern around a bar magnet. Then I used a Tesla coil to light up a fluorescent bulb placed close to it.

EM wave (dipole or half-wave). This type of wave involves both Electric and Magnetic Fields.

http://www.falstad.com/emwave1/ 

Streamlines of wind can be represented several ways. These are examples of velocity fields. The velocity has a direction and magnitude (speed in this case). Two sites that show maps like this are https://earth.nullschool.net/ and https://www.ventusky.com/

These were used to motivate the use of electric field-line patterns. Think of the apparent alteration of the space around a highly charged object due to the electric charge. This motivates the electric field. If you sprinkle iron filings on a piece of paper placed over a magnet you get a representation of a magnetic field, which you probably saw in your school science classes.

http://physics.bu.edu/~duffy/semester2/c02_field.html 

Electric dipole field lines (a dipole is a positive charge and negative charge near each other):

http://physics.bu.edu/~duffy/semester2/c02_fieldlines_dipole.html 

Moving charge applet. I showed acceleration of the charge along a line, and the idea that the field is delayed (retarded in time) compared to the movement of the source of the field (the charge).

http://www.cco.caltech.edu/~phys1/java/phys1/MovingCharge/MovingCharge.html 

Retarded Field Applet (This is hard to explain in words, you need to see me point at some of the features; the SHO option illustrates the production of electromagnetic waves. Retarded means something like delayed, and is a purely technical term in this context. There is no offense meant to anybody. The idea is that the field at some distance from the source is delayed, or more precisely retarded, to a later time. This was the original meaning of the word; something occurs at a later time than usual. So the fields seen at a distance from the source represent the fields that were produced when the source was at the position is was located at an earlier time t=d/v.) As these electric field lines get further from the oscillating source, they become transverse waves.

http://webphysics.davidson.edu/Applets/Retard/Retard_FEL.html 

Slow-motion EM wave. This is a different way of representing the fields at a large distance from the source. Notice that both electric and magnetic fields are needed to make the wave, because a changing magnetic field is need to produce an electric field, and a changing electric field is needed to produce a magnetic field (far from the sources). They are oriented transverse to the velocity and perpendicular to each other. The electric field can be oriented in different directions (perpendicular to the velocity) but the magnetic field then must be perpendicular to the electric field. This lead to the concept of polarization, which tells us which way the electric field is pointing.

http://www.walter-fendt.de/html5/phen/electromagneticwave_en.htm

Reflection and Refraction of Light occurs because light is a wave phenomenon. This illustrates why we get refraction when a wave changes its velocity:

http://www.walter-fendt.de/html5/phen/refractionhuygens_en.htm