HW

Find an expression for the Doppler effect for sound - something that allows one to predict the new frequency (or Doppler shift) based on speeds of moving objects and detectors.

Organ Pipes and Standing Waves

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

Play with the applet above, observing the wave with the tube open on both ends.  Then try one end open only.

Increase the number of harmonics and note how the wave shape changes.

This is important - the air molecules move as depicted in the animation on top.  The animation below represents graphs of air molecule motion (displacement) or pressure (if you click on that button).

Try these problems (E block, for Tuesday.  A block can hold off on trying these until after Monday's class.)

1.  A tube is open on both ends (as shown in class).  Assume that the speed of sound is 340 m/s.  The tube length is 0.5-m.  Find the following:

a.  the wavelength of the n=1 harmonic (lowest harmonic that fits in the tube)
b.  the frequency of this harmonic
c.  the frequency of the next 2 harmonics above n=1.  Assume that it basically works like a guitar string.

2.  If you wish a tube to vibrate at concert A (440 Hz), how long should it be?

That's it.  Sorry again (E block) that we started late today.

Clara Rockmore / theremin

http://www.youtube.com/watch?v=pSzTPGlNa5U

http://www.youtube.com/watch?v=b5cOdZh4zK8

http://www.youtube.com/watch?v=Bm-rnbupIjk

>

http://www.youtube.com/watch?v=QSLMWasU0rM

The Beach Boys with a "tannerin" -- sounds like a theremin, but is easier to play.

cool.

http://dish.andrewsullivan.com/2013/10/14/self-building-blocks/

Wait... did I post this already?

just cool.

http://www.slate.com/blogs/bad_astronomy/2013/10/21/three_illusions_that_will_destroy_your_brain.html

Wave practice pre-quiz

1.  Consider a string, 0.2-m long.  The fundamental frequency of this string is 40 Hz.
a.  Draw the first 3 harmonics.
b.  Calculate the wavelengths, frequencies and speeds of the harmonics.

2.  What is the wavelength of an 89.7 MHz radio wave?  (This problem has been edited to change frequency to wavelength.)

3.  Draw the resulting wave:  y = 2 sin x + 3 cos x.  Also, give the exact value of y when x = 90 degrees.

4.  Consider a triangle with sides:  33, 56, 65.  Find the values of the angles.

5.  What is the period of a 1.3-m long pendulum on Earth?  On the Moon?

All formulas will be given in this quiz - no need to memorize:  SOH CAH TOA, v = f l, l = 2L/n, c = 3E8 m/s

Sine wave fun

A block - quiz next Thursday.
E block - quiz next Wednesday

http://my.hrw.com/math06_07/nsmedia/tools/Graph_Calculator/graphCalc.html

This is the grapher used in class.

Also useful:

http://surendranath.tripod.com/Applets/Waves/TWave02/TW02.html

http://www.colorado.edu/physics/2000/applets/fourier.html

http://www.walter-fendt.de/ph14e/stwaverefl.htm

Just cool:

http://www.acs.psu.edu/drussell/Demos/TuningFork/fork-modes.html

https://www.youtube.com/watch?v=aWAjLOwOHU0

Beside the homework - stuff FYI (links from class, etc.)

http://www.youtube.com/watch?v=XKRj-T4l-e8
Glass harp guy

http://www.youtube.com/watch?v=cPALfz-6pnQ
Shattering glass with sound

http://www.alaska.net/~clund/e_djublonskopf/Flatearthsociety.htm
Whaaaaaa?????

HW for Wednesday (A) and Thursday (E)

Be sure that you are in DEGREES mode on your calculator.

1.  Revisit the Moon Problem.  If the diameter of the Moon is 1/4 the diameter of the Earth (look it up), and the angle subtended by the Moon is 0.5 degrees, how far away should the Moon be from Earth?

2.  Consider a 3-4-5 triangle.  Find the values of the angles in the triangle.

3.  This one may be trickier.  Make a graph of y = sin x, for values from 0 to 360 degrees.  You could do this on your calculator, but make sure that you could also do it "by hand" - choosing several x values (30, 45, 60, 90, 120, 135 degrees, etc.) and plotting them on an axis.  Graph paper may actually be best for this.

4.  Repeat 3 for y = cos x.

5.  How would the graphs for 3 or 4 above differ if there were coefficients?  Say, y = 3x.  How would the graph change?  (This is an amplitude change.)

6.  How would the graph change in this case:  y = sin(2x)

Lab Guidelines

Your first formal lab will be due in 3 classes.  If you want me to have a quick look at it, show it to me within 2 classes.

The lab writeup should have each of the following items:

Title of Experiment - this is up to you
Your name
Lab partner(s)
Date(s) performed

Purpose - the purpose of the experiment, as it appears to you

Data - in table form, with units.  Give table a title as well.

Graph(s), where relevant - for this harmonic lab, graphs are optional.  They may make your point(s) stronger.

Answers to lab questions - see lab handout

Sources of error and ways to eliminate/reduce error

General conclusion - Talk about what you learned in the experiment.  Analyze data.  Give thoughts and reasoning, where appropriate.  Talk about applications or places where this new knowledge applies.

It's not that different from the first lab - just a couple of extra things.  Make sure it is neat.

Waves - part 1

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

(Note that the 'l' above should be the Greek letter 'lambda'.)

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

c = f l

Again, the 'l' should be Greek letter 'lambda'.

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) or cm/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.

Interference

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 (as in, 1 sin x + 2 sin x = 3 sin x). Most cases are more complicated (1 sin x + 3 cos x = .....).

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.  Or if you prefer, f_n = n f₁.

one more thing

If you haven't played around with this yet, do so:

http://phet.colorado.edu/sims/wave-on-a-string/wave-on-a-string_en.html

Homework due after the retreat

1. Observe the image of "harmonics" from class below. Can you come up with an equation that represents/predicts the wavelength series, starting from the simplest/first wave?

2. Check out the electromagnetic spectrum chart. See if you can find out, doing some bits of research, where these devices reside in the spectrum: cell phones, garage door openers, sunlight, FM radio, AM radio, TV, any other waves of interest to you.

3. Define these words: harmonics, wave, radian