This document discusses standing waves and nodes and antinodes in musical instruments. It explains that nodes are points where the medium cannot move, such as the ends of a guitar string, while antinodes are points of maximum displacement that can occur at open ends. The length of an instrument determines which wavelengths can create standing waves, with half wavelengths fitting between two nodes or quarter wavelengths between a node and antinode.

1. Resonance and Musical Instruments Unit 8 Class 3 E. Alexander Burt

2. Review of Standing Waves Time to recall standing waves from the previous chapter. Remember the key characteristic of standing waves: nodes and antinodes At the node, there is no displacement of the medium At the antinode, the displacement is a maximum. Remember the spring lab?

3. Standing waves on physical systems Think about a guitar string. It is attached at each end. Because of this, the ends are not free to move. Therefore, there must be a node at each end. Now think about a tuning fork. The metal is attached at one end and not at the other. Therefore, there will be a node at the attached end and an antinode at the open end. Finally, think about a metal bar supported in the middle. Neither end is attached, therefore both ends will be antinodes.

4. In a nutshell… The points where the physical medium is unable to move – such as the ends of the guitar string – must be nodes. If the medium ends without being “tied down” the end will be an antinode.

5. Node – Node: what wave “fits?” If each end is a node, then any number of half waves will fit If the length of the string is L, then the formula is: L = n  /2 Solving for  we get:  = 2L / n

6. If each end is an antinode… The pattern is the same as if each end is a node. Any number of half waves will fit.

7. Node - Antinode How much of a wave is between a node and an antinode? ¼ of the wave. The next antinode happens at ¾ of the wave. Odd numbered quarter waves will fit. If the length of the resonant column is L, that means: L = n  / 4 where n = 1, 3, 5…