Organ pipes - sound in tubes

We will be talking about waves in tubes/pipes (like brass instruments, woodwinds, etc.).

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.