SPH3U UNIVERSITY PHYSICS

Transcription

1 SPH3U UNIVERSITY PHYSICS WAVES & SOUND L (P ) & Resonant Frequency Every object has a natural frequency or resonant frequency at which it will vibrate most easily. To keep a child moving on a swing, we must push the child with the same frequency as the natural frequency of the swing. 1 & Resonant Frequency RESONANT FREQUENCY frequency at which a medium vibrates most easily 2 1

2 & Resonant Frequency We use a similar technique to rock a car that is stuck in the snow. And when a large truck passes your house, you may have noticed that the windows rattle. 3 & Resonant Frequency These are all examples of a phenomenon called resonance or mechanical resonance. is the response of an object that is free to vibrate to a periodic force with the same frequency as the natural frequency of the object. RESONANCE also known as mechanical resonance response of an object that is free to vibrate to a periodic force with the same frequency as the natural frequency of the object 4 Activity: (Part 1) INSTRUCTIONS A. Place two mounted tuning forks close to and facing each other. B. Sound one of the forks and then dampen its vibration with your hand. 5 2

3 Activity: (Part 1) 1. What did you hear after you dampened the fork? 6 Activity: (Part 1) 2. Where is the sound coming from? Why? When the first tuning fork is struck and then silenced, a sound of the same frequency comes from the second fork even though it has not been struck. has occurred because the forks have the same natural frequency. Energy has been transferred from one fork to the other by sound waves. 7 Activity: (Part 1) 3. Explain how resonance is essential to human hearing? 8 3

4 Activity: (Part 2) INSTRUCTIONS A. (mechanical) can also be demonstrated with a series of inverted pendulums. Watch the video carefully as the pendulums are set in motion. 9 Activity: (Part 2) 1. Why did the pendulums of the same colour vibrate together? since they had the same length they also had the same natural frequency 10 Activity: (Part 2) 2. Assume you have a series of pendulums suspended from a stretched string. When A is set in vibration, which sphere(s) will also begin to vibrate with the same frequency? Why? E since it has the same length as A it also has the same natural frequency 11 4

5 Activity: (Part 2) 3. What about B? C? B D C none 12 When one object vibrates in resonance with another object, it is called a sympathetic vibration. There are many instances in the world of sympathetic vibrations some planned for and useful and others not so useful. SYMPATHETIC VIBRATION occurs when one object vibrates in resonance with another of the same resonant frequency 13 Mechanical resonance must be taken into account when designing bridges, airplane propellers, helicopter rotor blades, turbines for jet engines, plumbing systems, and many other types of equipment. A dangerous resonant condition may result if this is not done. 14 5

6 For example, rockets can develop longitudinal vibrations during launch. During launch, the propellant pipes can experience low-frequency disturbances which periodically change the propellant flow rate. This in turn affects the thrust of the rocket. Normally, the mass of the rocket is so large that the variations in thrust cause very little change in acceleration, so this effect goes unnoticed. However, if the frequency of the thrust vibrations matches the natural or resonant frequency of the rocket, then resonance can take place. In this case, the rocket will feel like it is surging back and forth like a pogo stick. This is known as the pogo effect. 15 In 1841, a troop of British soldiers marched in step across a bridge, which created a periodic force that set the bridge in resonant vibration and caused the bridge to collapse. 16 Large vibrations in buildings can be caused by earthquakes. For most areas, however, they are caused by wind. Wind can cause some skyscrapers to sway up to 1 m at the top floor. It is the elasticity of the structure that allows it to vibrate. This is known as aeroelastic flutter and occurs when more energy is added to the vibrations than can be lost to the natural damping of the structure. Aeroelastic flutter, or simply flutter, is the most dangerous type of vibration in aircraft. 17 6

7 If an opera singer sings a note with the same natural frequency as that of a wineglass, the glass will begin to vibrate in resonance. If the sound has a high enough intensity, the wineglass could vibrate with an amplitude large enough that it shatters. 18 Radio and television provide another example of resonance. When you tune a radio or television, you are actually adjusting the frequency of vibration of particles in the receiver so that they resonate with the frequency of a particular signal from a radio or television station. 19 The human body also has resonant frequencies. Experiments have shown that the entire body has a mechanical resonant frequency of about 6 Hz, the head of between 13 Hz and 20 Hz, and the eyes of between 35 Hz and 75 Hz. Large amplitude vibrations at any of these frequencies could irritate or even damage parts of the body. 20 7

8 For these reasons, engineers are careful to avoid situations where resonance might occur within structures. They must carefully analyze structures to determine their resonant frequencies. While a building may not fall down as a result of such vibrations, other effects such as metal fatigue can occur that can damage the structure. 21 MECHANICAL RESONANCE natural phenomenon which includes: aeroelastic flutter in aircraft, buildings, vehicles,... pogo effect in rockets considered when designing structures, buildings,... techniques to dampen unwanted vibrations are employed 22 Damping & Damping is a reduction in the amplitude of a wave as a result of energy absorption or destructive interference. For example, the child and swing will not move indefinitely. Once you stop pushing, the child-swing system will eventually come to rest due to friction and air resistance. The swing motion has been dampened. 23 8

9 Damping & We can observe the absorption of wave energy by a medium as a reduction in the amplitude the wave. 24 Damping & Damping is sometimes desirable. You may want to reduce the effects of a vibration so that sound will not carry from one room to the next, or in a complicated structure such as a car or building, where the effects of strong vibration can be dangerous. DAMPING condition in which the amplitude of a wave is reduced two methods: Î the medium removes energy from the wave Ï destructive interference reduces its amplitude 25 Damping & To help decrease the amplitude of vibrations due to resonance, some buildings have a mass damper, usually consisting of large shock absorbers or a pendulum made out of concrete or steel. These dampers develop sympathetic vibrations, which take energy from the building when it vibrates, thus decreasing its amplitude. The dampers are designed to take the energy before it can return to the building. 26 9

10 Activity: (Part 3) INSTRUCTIONS A. Fill a styrofoam cup with water. Leave a small amount of space. B. While holding the cup steady walk with a slow steady space. Do not change your pace or the method with which you are carrying the beaker. C. If necessary, refill your beaker. D. Repeat step B with a fast pace. E. Repeat steps B through D but now attempt to control the spillage. F. Clean up any spills. This activity is best performed outside! 27 Activity: (Part 3) 1. What did you notice? 2. Did you notice anything about the amount of spillage between a slow and fast pace? 3. How did you control the spillage? 28 U Check Your Learning TEXTBOOK P.432 Q.1,3 P.465 Q.2 P.471 Q.2,