I was walking through my local home supply store the other day carrying a 10 ft length of plastic pipe. The pipe was horizontal and my hand was supporting the middle of the pipe. I noticed that when I took two steps each second the ends of the pipe would move up and down a large distance. If I walked a little slower or a little faster they did not. Explain why this happened. What is the physical phenomenon being represented here? Were the ends of the pipe nodes or antinodes? What other rates of walking might also cause increased vibration in the pipe?
The phenomenon was resonance and the ends of the pipe were antinodes. The length of the pipe was an integral multiple of 1/2 of the wavelength. Other integral multiples of the walking speed could cause resonances.
The phenomenon you observed with the ends of the pipe moving up and down when you walked at a specific rate is known as resonance. Resonance occurs when the frequency of an external force matches the natural frequency of an object, resulting in a significant increase in vibrations.
In this case, the pipe was acting like a simple pendulum, where the natural frequency of oscillation depends on its length. The longer the pipe, the lower the natural frequency. When you walked at a specific rate, the up and down motion of your steps introduced a periodic force into the system. If the frequency of your steps matched the natural frequency of the pipe, the pipe experienced resonance and exhibited large oscillations.
The ends of the pipe acted as antinodes, which are points of maximum displacement, while the middle of the pipe remained relatively stationary. This means that the ends of the pipe moved the most during the resonance.
To find other rates that might also cause increased vibrations, you need to consider the natural frequency of the pipe. If you walked at a rate that is a multiple of the resonant frequency (e.g. double or triple the resonant frequency), you would likely observe increased vibration in the pipe. Walking at rates significantly different from the resonant frequency would not produce resonance and therefore not cause large oscillations.
In summary, the physical phenomenon represented here is resonance, where the frequency of your steps matches the natural frequency of the pipe, resulting in increased vibrations. The ends of the pipe acted as antinodes, and other rates of walking that are multiples of the resonant frequency could also cause increased vibration in the pipe.