# Newton’s Third Law and The Secret Physics of Drumming

Dating back to 4000 BC in Egypt, drums are the oldest known instrument in the world. Not only have people been using drums for a long time, but Macaque monkeys also use drumming to show dominance and communicate. Drums have been used all over the world as a method of communication or a way to create music. People who play the drums heavily rely on the physics behind them, but many people never truly realize how much newton’s third law takes place in their activity. When a person plays drums, to simply put it, they are just hitting drums in different ways at different times. The main thing they are doing is bouncing a stick, a hand, a mallet or something similar off of a drum. Without being able to bounce something off the drum, drumming would be drastically different, or already non-existent in this day and age.

Both the sticks, mallets, hands, etc., and the makeup of the drum itself have major roles in the physics of drumming. For example, without Newton’s Third Law, the drumstick would never bounce off the drum, leaving drums having a dull and bland smacking noise. Newton’s Third Law states that every action has an equal and opposite reaction. The action would be the sticks hitting the drum, and the equal and opposite reaction are the sticks bouncing off the drum. As the sticks push against the drumhead, the drumhead also pushes against the sticks with an equal and opposite force, leaving the drum resonating with sound and the sticks back up in the air. This is possible because of the tension in the circular membrane of the drumhead. The tension makes it easier for the sticks to apply more force to the drumhead and make a louder sound while being pushed back up to hit again. Different drums also have different ways they need to be hit. For example, the snare drum needs to be hit in the center, while the timpani drum needs to be hit near the sides.

The ideal circular membrane has a basic frequency of ƒ1=0.765((√ T/σ)/D), where ƒ = frequency, T = membrane tension, σ = mass per unit, and D = the diameter of membrane. With this ideal frequency, it is easiest and most efficient to hit the drumstick off of the drum. Leading back to Newton’s Third Law, when it is most efficient to hit the drumstick off of the drumhead the forces of the sticks and the drum are completely equal and the drum leaves a resonating sound as the stick goes back up the be used to hit the drum again.

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