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.