#wavephenomena

[wtfearth123]

This string shooter uses two wheels on motors to push a string forward while a tube guides the string back through the wheels, creating a constant loop that appears to defy gravity & demonstrates wave phenomena.

The string shooter is a fascinating device that can be used to demonstrate various physics concepts, such as air drag, wave phenomena, and hydraulic jump. It consists of a pair of counter-rotating wheels that propel a closed loop of string at a constant speed. The string loop forms a stable shape that remains suspended in the air, seemingly defying gravity. How does this device work and what are the physics behind it?

One way to understand the string shooter is to consider the forces acting on each segment of the string loop. The string is subject to three main forces: tension, gravity, and air drag. Tension is the force exerted by the wheels on the string, which keeps it moving forward. Gravity is the downward force due to the mass of the string, which tends to make it fall. Air drag is the resistive force due to the interaction of the string with the surrounding air, which opposes its motion.

The balance of these forces determines the shape and stability of the string loop. At low speeds, gravity dominates over tension and air drag, and the string hangs down like a pendulum. As the speed increases, tension becomes more important and the string rises up. At some critical speed, tension and gravity cancel out, and the string becomes horizontal. This is similar to what happens when a rope is spun around by hand.

However, at higher speeds, something interesting happens. The string loop does not remain horizontal, but bends upward into a self-supporting loop. This is because air drag becomes significant and creates a lift force on the string. The lift force is perpendicular to both the direction of motion and the direction of gravity, and acts as a centripetal force that keeps the string in a circular path.

The shape of the string loop can be described mathematically by using some simplifying assumptions. One assumption is that the string has a negligible radius and mass compared to its length and speed. Another assumption is that the air drag is proportional to the square of the speed and depends on the angle between the string and the airflow. Under these assumptions, one can derive a differential equation that relates the curvature of the string to its speed and angle.

The solution of this equation reveals some interesting features of the string loop. One feature is that there is a critical point on the loop where the speed of the string matches the speed of sound in air. This point separates two regions: a supercritical region where the speed of the string is greater than the speed of sound, and a subcritical region where it is lower. In the supercritical region, any disturbance on the string cannot propagate upstream, while in the subcritical region, it can.

Another feature is that there are two types of solutions for the shape of the loop: regular solutions and singular solutions. Regular solutions are smooth and continuous, while singular solutions have a sharp turn at the critical point. The regular solutions are analogous to hydraulic jumps in fluid dynamics, where a fast-moving stream transitions to a slow-moving one through a shock wave. The singular solutions are more realistic and correspond to what is observed experimentally.

The string shooter is an example of how simple devices can reveal complex physics phenomena. It shows how air drag can create lift and stabilize a loop of light string in mid-air. It also shows how supersonic and subsonic regimes can coexist on a single object, creating a critical point where waves cannot propagate. The string shooter is not only fun to watch, but also educational to analyze. I hope you enjoyed reading & learning about the string shooter. 😊🙏