Lect-2010-030311

Lect-2010-030311 - SLHS 2010 Resonance 3 Mar, 2011...

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Unformatted text preview: SLHS 2010 Resonance 3 Mar, 2011 Resonance Resonance is defined as the increase in amplitude that occurs when an object vibrates at its preferred frequency. What does that mean? Preferred Frequency All objects have a preferred frequency, based on their physical characteristics. Earlier we talked about four examples of SHM. Pendulum Mass on a Spring Tuning Fork Vibration of an Air Mass How do these examples illustrate preferred frequency? Pendulum The frequency with which a pendulum vibrates depends on its length T = period L = length g = acceleration due to gravity (constant) f = 1/T Mass on a Spring The frequency of a mass on a spring is determined by the mass of the object and the elasticity of the spring. f = /2 = k/m = angular frequency k = spring constant m = mass of object Tuning Fork The frequency with which a tuning fork vibrates depends on: The length of the tines, The thickness of the tines, The material the tuning fork is made with. Mechanical Resonance The examples thus far have all been mechanical systems. The frequency formulas vary, but they are all directly determined by physical properties of the system . If an external force is applied at the right time during a cycle, you can cause an increase in amplitude. Child on a Swing A child on a swing is essentially a pendulum. It will vibrate at a frequency determined by its length. If you push the swing at the top of the arc (maximum displacement), you can cause an increase in amplitude. However, this external force will not alter the frequency. This increase in amplitude is called resonance . Tacoma Narrows Bridge Collapse Incident where mechanical resonance caused major damage. External forcewind at a constant 42 mph, causing vibration at 0.2 Hz. http://www.youtube.com/w Mechanical Resonance When an external force is applied to a system vibrating in SHM, its amplitude increases, but its frequency stays the same. How does this relate to sound? Resonance of an Air Mass Air itself can vibrate in response to sound at any frequency. However, if the air mass is enclosed, it will resonate at a frequency determined by the physical properties of the container. Acoustic Resonance Acoustic Resonance We can demonstrate resonance by blowing into a partially filled bottle. When we do this, two things happen: 1. The sound going in is pretty quiet, but the sound coming out is much louderthat is, there is an increase in amplitude. 1. The sound going in is pretty noise-like, consisting of multiple frequencies, but the sound that comes out is at a specific frequencythat is, the sound is filtered. Acoustic Resonator Air in a container (or cavity) resonates....
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Lect-2010-030311 - SLHS 2010 Resonance 3 Mar, 2011...

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