HW

C block - write and solve your own Dopper effect problem. It should have at least 4 parts, like the class example.

E block - same as earlier post. Find and interpret an equation for the Doppler effect.

Happy 3 day weekend!

Homework revisited

Doppler effect:

E block - find (and interpret) an equation for the Doppler effect

C block - define (formally) the Doppler effect and find an equation that represents it. Same as the previous blog entry.

Doppler Effect HW

Come to class with a working definition of the Doppler effect (equation optional).

Play with these applets:

http://www.lon-capa.org/~mmp/applist/doppler/d.htm

http://falstad.com/mathphysics.html

Run the Ripple tank applet -

http://falstad.com/ripple/

Homework

Practice for the upcoming quiz - which is class after next

1. Consider a string, 0.4 m long. The normal wave speed is 120 m/s. Find the wavelengths and frequencies of the first 3 harmonics. Draw the standing waves as well.

2. repeat the first problem for a tube open at both ends, if it is 0.8 m long and the speed of sound is 340 m/s.

3. Consider problem 2 - what would happen if the tube were capped on one end.

4. Consider a concert A - 440 hz. Find these frequencies:

A. The next 2 A notes
B. The note immediately after A.
c. The note 3 piano keys after A

Awesome.

http://www.youtube.com/watch?v=i31godfcZZ0&feature=relmfu

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

Watch these!

And watch for more homework being assigned later today.

C block physics (IN CLASS) and E block physics homework

Folks - I'm out this morning. Here are notes for today's class:

We will be talking about waves in tubes/pipes (like brass instruments, woodwinds, etc.). Play around with the animations and take notes.

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

http://ralphmuehleisen.com/animations.html


Ultimately, I want you to see that waves in a tube are the same (mathematically) as waves on a string - the biggest differences:

the waves are longitudinal/compressional, NOT transverse
the waves have antinodes at each end, NOT nodes

When an organ pipe/tube is open on both ends, you have antinodes (in a longitudinal wave) on both ends. This becomes (mathematically) the same as a vibrating string (though the string has nodes on both ends). The math looks like the same, however:

lambda (l) = 2L/n

The lowest harmonic (f1, where n = 1) is still found by using v = f l, and dividing v by l. Successive harmonics are 2f1, 3f1, 4f1, ....

So, a tube has a lowest possible resonant tone, but if air is pushed through it harder, higher harmonics can be heard. Think about the recorder - you may have learned how to play one in your younger years. Keeping your fingers in the same positions, but blowing a bit harder, gives higher tones.

Some things to try:

Work your way through lessons on PhysicsClassroom.com

http://www.physicsclassroom.com/Class/sound/

PARTICULARLY LESSONS 5c and 2a.

Here is a problem to try:

1. Consider a tube that is 0.8-m long. The speed of sound is 345 m/s. Find the following:

a. the wavelengths of the first 4 harmonics
b. the frequencies of the first 4 harmonics
c. the wave shapes of the first 5 harmonics - see the applet, as well as my note sheet below

Note that the mathematics in this problem are IDENTICAL to those of the standing waves in the string - the speed, however, is the speed of sound.

wave addition

Homework for C block (due M0nday)
Homework for E block (due Tuesday)

Add (or subtract, as the case may be) the following waves (either on paper or on calculator):

sin x + 2 sin x

sin 2x - sin x

(Note that the 2 in sin 2x refers to the frequency.)

sin x + 2 cos x

2 sin 2x + 3 cos 3x

4 sin x - 2 cos 2x

Now, I'm no wave snob - feel free to try your own instead of mine!

Ultimately, you're generating a "superposed" wave - a third wave that is the mathematical sum of the original waves.

Of course, you can add more than just 2 waves....

2 sin x + 3 cos 2x - sin 4x

And we haven't even talked about phase differences. Consider the difference between these waves:

sin x
sin (x + 45)

Can you see the difference?

Play and comment.

One more thing to check out....

..... after you've done the homework (on the previous blog entry):

http://www.youtube.com/watch?v=kBmRNkM9saA&feature=related

(That's from my class.)


These are not from my classes:

http://www.youtube.com/watch?v=JgKzx3tZ59A&feature=related

http://www.youtube.com/watch?v=YedgubRZva8&feature=related

http://www.youtube.com/watch?v=DGSU5rcHmRQ&feature=related

Wave addition

Folks,

Please play around with the following applets. Write down some comments - anything you find interesting, anything you learn, etc. Play around with the applets. Make comments.

Two things to keep in mind - one is very important. WHAT IS SUPERPOSITION (AKA Wave addition)? Another (less important) thing to consider: What are beats?


1. Observe what happens when two (positive amplitude) wave pulses interact.

http://www.phy.ntnu.edu.tw/ntnujava/index.php?topic=18

2. Then look at this one:

http://www.phy.ntnu.edu.tw/ntnujava/index.php?topic=19.0

3. Now this one:

http://webphysics.davidson.edu/applets/superposition/GroupVelocity.html

4. Here are some more details to examine:

http://www.kettering.edu/physics/drussell/Demos/superposition/superposition.html

http://zonalandeducation.com/mstm/physics/waves/interference/waveInterference2/WaveInterference2.html

5. More complex, but cool:

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

6. Also:

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

7. If you have time, check this out:

http://falstad.com/mathphysics.html

Click on the first link (Ripple Tank 2-d wave applet). Play around.

Enjoy!

wave problems - try all

Some review questions from the first 3 weeks.

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

2. Differentiate between longitudinal and transverse waves. Give examples.

3. Draw a wave and identify (or define) the following parts: crest, trough, amplitude, frequency, period.

4. What is the frequency of a wave that travels at 25 m/s, if 3 complete waves can fit in a 10-m space?

5. Draw the first 3 harmonics for a string that is 3-m in length. Also, find the first 3 frequencies and wavelengths, if the wave speed is 100 m/s.

6. The speed of sound (in air) is approximately 345 m/s. If you stand far from a mountainside and yell at it, the echo returns to your ear in 1.8 seconds. How far is the mountain from you?

7. Approximately how much greater is the speed of light than the speed of sound in air?

8. Discuss the physics of the Chladni plate.

9. Find the wavelength of a 89.7 MHz radio wave.

Draft due

Don't forget, both C and E block physics -

The draft of Lab 1 is due next class.

It is NOT required, but is strongly recommended. Also, the final version of this lab will be due the next class. There will likely be no time in class to work on it.