post-quiz HW

Read about the Doppler effect.  If possible, find an equation that describes it and identify the variables involved.

Standing wave applet from today's class

http://www.physics.smu.edu/~olness/www/05fall1320/applet/pipe-waves.html

Practice for Friday's quiz

1.  Differentiate between mechanical and electromagnetic waves.  Give examples.

2.  Draw a wave and identify the primary parts.

3.  Find the speed of a 500 Hz wave with a wavelength of 0.4 m.

3.  What is the frequency of a wave that travels at 24 m/s, if 3 wavelengths of the wave fit in a 12-m space.  (Hint:  find the wavelength first.)

4.  Approximately how much greater is the speed of light than the speed of sound?

5.  Draw the first 3 harmonics for a wave on a string.  If the length of the string is 1-m, find the wavelengths of these harmonics.

6.  Show how to compute the wavelength of WTMD's signal (89.7 MHz).  Note that MHz means 'million Hz."

7.  Explain the Chladni plate seen in class.

8.  A C-note vibrates at 262 Hz (approximately).  Find the frequencies of the next 2 C's (1 and 2 octaves above this one).

*9.  Given a 440 Hz concert A, find the following frequencies:  one octave below, the note A# (one semi-tone above), the note B (2 semi-tones above).

*10.  Explain the Ruben's tube from class.

*11.  Consider an organ pipe 0.5-m long.  If the speed of sound is 340 m/s, find (and draw) the first 3 harmonics (wavelengths and frequencies).

Wave applets

http://www.smaphysics.ca/phys30s/waves30s/waveadd1.html

http://www.udel.edu/idsardi/sinewave/sinewave.html

Recent notes on waves

There are 2 primary categories of waves:

Mechanical – these require a medium (e.g., sound, guitar strings, water, etc.)

Electromagnetic – these do NOT require a medium and, in fact, travel fastest where is there is nothing in the way (a vacuum).  All e/m waves travel at the same speed in a vacuum (c, the speed of light)

General breakdown of e/m waves from low frequency (and long wavelength) to high frequency (and short wavelength):

Radio

Microwave

IR (infrared)

Visible (ROYGBV)

UV (ultraviolet)

X-rays

Gamma rays

In detail, particularly the last image:

http://hyperphysics.phy-astr.gsu.edu/hbase/ems1.html

http://csep10.phys.utk.edu/astr162/lect/light/spectrum.html

http://www.unihedron.com/projects/spectrum/downloads/full_spectrum.jpg

Waves have several characteristics associated with them, most notably:  wavelength, frequency, speed.  These variables are related by the expression:

v = f l

speed = frequency x wavelength

For e/m waves, the speed is the speed of light, so the expression becomes:

c = f l

Note that for a given medium (constant speed), as the frequency increases, the wavelength decreases.

Note the units:

Frequency is in hertz (Hz), also known as a cycle per second.

Wavelength is in meters or some unit of length.

Speed is typically in meters/second (m/s).

Sound waves

In music, the concept of “octave” is defined as doubling the frequency.  For example, a concert A is defined as 440 Hz.  The next A on the piano would have a frequency of 880 Hz.    The A after that?  1760 Hz.  The A below concert A?  220 Hz.  Finding the other notes that exist is trickier and we’ll get to that later.

Waves can “interfere” with each other – run into each other.  This is true for both mechanical and e/m waves, but it is easiest to visualize with mechanical waves.  When this happens, they instantaneously “add”, producing a new wave.  This new wave may be bigger, smaller or simply the mathematical sum of the 2 (or more) waves.  For example, 2 identical sine waves add to produce a new sine wave that is twice as tall as one alone.  Most cases are more complicated.

In music, waves can add nicely to produce chords, as long as the frequencies are in particular ratios.  For example, a major chord is produced when a note is played simultaneously with 2 other notes of ratios 5/4 and 3/2.  (In a C chord, that requires the C, E and G to be played simultaneously.)  Of course, there are many types of chords (major, minor, 7ths, 6ths,…..) but all have similar rules.  In general, musicians don’t remember the ratios, but remember that a major chord is made from the 1 (DO), the 3 (MI) and the 5 (SO).  It gets complicated pretty quickly.

We looked at specific cases of waves interfering with each other – the case of “standing waves” or “harmonics.”  Here we see that certain frequencies produce larger amplitudes than other frequencies.  There is a lowest possible frequency (the resonant frequency) that gives a “half wave” or “single hump”.  Every other harmonic has a frequency that is an integer multiple of the resonant frequency.  So, if the lowest frequency is 25 Hz, the next harmonic will be found at 50 Hz – note that that is 1 octave higher than 25 Hz.  Guitar players find this by hitting the 12^th fret on the neck of the guitar.  The next harmonics in this series are at 75 Hz, 100 Hz and so on.    

lab report homework

Lab draft (whatever you have) is due Thursday.  The formal lab will be due TWO classes after that - I think that puts it right after the "In-Mind" days.

Follow the lab guidelines from the earlier post.

Your conclusion should focus on these things:

- What trends can be seen?

- What mathematical relationship(s) can be seen?

- What specific errors are present?

- What can you conclude from the lab?

- Does this have practical applications in real life, and/or is this related to something you've seen before?

Formal lab guidelines - read these and begin to prep your lab

Formal lab guidelines

A draft lab will be due in TWO classes (Thursday), though drafts are generally optional.  The final formal lab will be due in THREE classes (next Monday).

Lab format. 

Typically, each lab should have the following items:

Title  (made up by you)
Your name
Lab partner name(s)
Date performed

Purpose of experiment - a line or two telling me the purpose of your work

Hypothesis (when asked for) - what do you anticipate will be true?

Introductory remarks - "In this experiment, we blah blah blah...." These can be short - it's the place where you say anything special about your approach to the problem.

Data tables - don't forget units

SAMPLE calculation, including relevant formulas used

Graphs, where relevant - there may be no relevant graphs for the wave lab. That part is up to you. Don't forget the units and axis labels.

Conclusion - To me, this is the meat of the lab report. Here are questions to consider:

Discuss the extent to which your hypothesis was validated (or rejected).
Discuss sources of error - be specific. Saying "human error" is somewhat meaningless.
Give suggestions for improvement.
Tell me something you learned and/or liked about the experiment.

The conclusion may be a few paragraphs or a couple of pages (or more, if you write a lot). Be specific, write well, use good grammar and spelling, etc.

In every case, you will be encouraged (but not required) to submit a draft lab. I will get it back to you the same day (in your mailbox) with some comments. The formal lab is typically due the class after that.

Points are deducted for late labs, unless there are extenuating circumstances.

Lab preparation

During our next class, we will investigate the phenomenon of waves on a string - specifically, harmonics on a string.

You will be using the apparatus demonstrated in class.  It generates electronic sine waves which are sent to a vibrating device - the device vibrates at the frequency specified on the sine wave generator.

Your goal will be to determine how the frequency, wavelength, harmonic number (number of half-waves or "humps"), speed and (possibly) string tension (as determined by the weight on the string).

Here are things to think about prior to the lab:

1.  How does the frequency (or pitch) depend on the tension in the string?
2.  How can we generate "harmonics" on a string?
3.  Looking at a standing wave, how could we determine the wavelength of the wave on that string?
4.  What type of mathematical relationship(s) might exist between the variables above?
5.  Look at some applets that demonstrate standing waves or harmonics on a string.  I will post some shortly.

homework

Questions to prepare for next class:

What is the current SI standard of the kg based on?

What is wave interference?

What are "standing waves"?   Are they related to "harmonics"?

Several days ago, you played with an applet designed to show you something about waves.  You may wish to revisit it, if that is helpful, to make your own standing waves.

SI units/standards

Mass is measured based on a kilogram (kg) standard.
Length (or displacement or position) is based on a meter (m) standard.
Time is based on a second (s) standard.

How do we get these standards?

Length - meter (m)

- originally 1 ten-millionth the distance from north pole (of Earth) to equator
- then a distance between two fine lines engraved on a platinum-iridium bar
- (1960): 1,650,763.73 wavelengths of a particular orange-red light emitted by atoms of Kr-86 in a gas discharge tube
- (1983, current standard): the length of path traveled by light during a time interval of 1/299,792,458 seconds

That is, the speed of light is 299,792,458 m/s. This is the fastest speed that exists. Why this is is quite a subtle thing. Short answer: the only things that can travel that fast aren't "things" at all, but rather massless electromagnetic radiation. Low-mass things (particles) can travel in excess of 99% the speed of light.

Long answer: See relativity.

Time - second (s)

- Originally, the time for a pendulum (1-m long) to swing from one side of path to other
- Later, a fraction of mean solar day
- (1967): the time taken by 9,192,631,770 vibrations of a specific wavelength of light emitted by a cesium-133 atom

Mass - kilogram (kg)

- originally based on the mass of a cubic decimeter of water
- standard of mass is now the platinum-iridium cylinder kept at the International Bureau of Weights and Measures near Paris
- secondary standards are based on this
- 1 u (atomic mass unit, or AMU) = 1.6605402 x 10^-27 kg
- so, the Carbon-12 atom is 12 u in mass

Volume - liter (l)

- volume occupied by a mass of 1 kg of pure water at certain conditions
- 1.000028 decimeters cubed
- ml is approximately 1 cc

Temperature - kelvin (K)

- 1/273.16 of the thermodynamic temperature of the triple point of water (1 K = 1 degree C)
- degrees C + 273.15
- 0 K = absolute zero

For further reading:

http://en.wikipedia.org/wiki/SI_units

http://en.wikipedia.org/wiki/Metric_system#History

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In addition, we spoke about the spherocity of the Earth and how we know its size. I've written about this previously. Please see the blog entries below:

http://howdoweknowthat.blogspot.com/2009/07/how-do-we-know-that-earth-is-spherical.html

http://howdoweknowthat.blogspot.com/2009/07/so-how-big-is-earth.html