Resonance Lab - University of Michigan



Instructor Outline: ResonanceUM Physics Demo Lab 07/2013Lab length: 70 minutesLab objective: Instruct the students about period, frequency, amplitude, wave velocity, resonance, simple harmonic motion (pendulum) and standing waves.Materials1 length of string2 nuts (pendulum bobs)1 ring stand1 stopwatch1 piston assembly1 small plastic storage tub (piston support)2 tuning forks – one labeled, one unknown1 measuring tape1 ruler1 calculator1 digital scaleExploration stage: 20 minutes - Group Lab WorkThe students work in groups to build pendulums. They test which variables affect the period.Analysis stages: 15 minutes – LectureSimple Harmonic Motion is presented for a mass on a spring and for the simple pendulum. The concepts of period, frequency and amplitude are introduced for oscillations.Application stage: 25 minutes – Group Lab WorkThe students observe resonance with resonance chambers. They calculate the speed of sound with a known frequency tuning fork, and then calculate the frequency of an unknown fork. The students draw upon the concepts introduced in the previous Waves Lab, including nodes, anti-nodes, overtones and wave diagrams for standing waves in tubes.Summary: 10 minutes – Lecture and DemonstrationThe Tacoma Narrows bridge disaster is presented and a wine glass shattered as a final demonstration of the potential danger that exists if structures are accidently driven at resonance.Suggested Demos:3A60.10 - Tacoma Narrows Video Clip3D40.55 - Shattering the Wine Glass3D32.10 - Organ Pipes3C55.U1 – Helium Voice3A40.31 – Linear Projection of Rotational Motion-Waves on a String Apparatus from Previous Waves Lab -Assorted Masses and springs to Demonstrate Dependency of Frequency on K and m for a Simple Harmonic Oscillator-Microphone and Visual Analyzer Oscilloscope program to show Fourier spectrum of various sounds—tin whistle, train whistle, harmonica, tuning fork and organ pipe.Concepts Developed:Mechanical systems have natural frequencies at which they will oscillate if disturbed.Period and frequency describe the behavior in time of oscillating systems. The relationship between the frequency f (number of oscillations/second) and the period T (number of seconds/oscillation) is.Amplitude is the magnitude of the oscillation and is independent of the frequency.The natural frequency for mass-and-spring oscillator is where k is the Hooke’s Law spring constant (Newtons/meter).The natural frequency for a pendulum is where g is the acceleration of gravity and L is the length of the pendulum. The frequency does not depend on the mass of the pendulum bob.The natural frequency of a mass-and-spring system does not depend on the acceleration of gravity and will be the same everywhere in the universe.The frequency of a pendulum depends on the acceleration of gravity and will therefore be different on different planets. The frequency or period of a pendulum can be used to perform sensitive measurements of the local acceleration of gravity on Earth or any other planet.Resonance occurs when the driving frequency of an external force applied to an object or system matches the natural frequency of the system. The amplitude of oscillations will grow with time if a system is driven at resonance, since the system is absorbing more energy as it is driven.One can measure the speed of sound with a known frequency tuning fork and a chamber. ................
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