Music Trajectories

Trajectories are essential to the science of music performance, but music majors rarely study the physics of motion. Consider the following graph of a conductor beating in 4/4 time:

Discussion Questions

1. Draw a picture of the conductor from the camera's view. Label the points at which each of the beats are located. 
2. How is it possible on the graph to determine the change of direction of the baton? 
3. What is the form of mathematics which describes changes in motion? 
4. What is the maximum velocity of the baton? 
5. Is the acceleration of the baton 0 at any point in the graph? If so, what are the coordinates? 
6. Comparing the minimum and maximum points, does the baton move a greater absolute distance in the x or y direction? 
7. What is the total length of trajectory of the baton in the x direction? In the y direction? 
8. Calculate the difference between initial and final positions of the baton. 

Additional graphs of music performance can be located in Volume 3 of How Do You Play That Thingamabob? The Science of Music Performance from Schottenbauer Publishing. These graphs can be integrated into music education curricula from late elementary school through high school and college/university.


Additional Information

Schottenbauer Publishing

Free Education Resources

Science of Music Memorabilia

Celebrate science of music with memorabilia from Zazzle! Colorful graphs from Schottenbauer Publishing are featured on these mugs, magnets, keychains, & postcards. Graphs include conducting, voice, piano, violin, recorder, flute, clarinet, saxophone, trumpet, trombone, drums, cymbal, and Tibetan bowl. A direct link is included below:

A variety of other STEM education collections are also available from Schottenbauer Publishing on Zazzle, which features regular sales on most items.  


Additional Information

Schottenbauer Publishing 

Free Education Resources