# Lec15 - Today Chapter 19(Vibrations and Waves Vibrations...

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Today: Chapter 19 (Vibrations and Waves)

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Vibrations Some Preliminaries Vibration = oscillation = anything that has a back-and-forth to it Eg. Draw a pen back and forth over the same line, repeatedly: When you come back to the same point defines one cycle, one vibration If do it faster, your “ frequency ” is higher, your “ period ” is less. But your “ amplitude (max. displacement) is the same – it’s bigger if the line is bigger. (We’ll come back to these terms shortly) Wave = vibration in both space and time i.e. goes from one place to another: A vibration that propagates in space
Vibration of a pendulum Suspend a stone at the end of a string and let it swing to and fro through small distances – makes a simple pendulum. Very regular oscillations if little friction – eg found in some clocks. Period = time of a to-and-fro swing (i.e a cycle) For pendulum, period only depends on its length The longer the length, the longer the period, i.e. takes more time to come back. i.e. swings less frequently. Period does not depend on the mass. Quite analogous to the free-fall and inclined planes of Galileo – all masses fall at the same rate in vacuum; also all masses swing back and forth on end of a same-length string at the same rate. DEMO – swing various objects from a string and test not mass- dependent but is length-dependent. Also depends on the value of g eg the same pendulum oscillates slower on the moon than on earth

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Clicker Question Is the time required to swing to and fro on a playground swing longer or shorter when you stand rather than sit? A) Shorter B) Longer C) The same Answer: A When you stand, the pendulum is effectively shorter, because the center of mass of the pendulum
Wave Description Simple harmonic motion – describes pendulum as well as more general wave-like motion. Eg a vertical spring with a mass at the end. Hold pendulum bob with ink at the end over a conveyer belt, it traces out a sine wave : (shown here is spring but same principle…) crests (high points) troughs (low points) So: Amplitude = maximum displacement from equilibrium (ie to crest or to trough) , and Wavelength = crest-to-crest distance , or, distance btn any successive identical parts equilibrium (middle)

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Wave description cont. Frequency = the number of to-and-fro vibrations in a given time (usually in a second). One vibration per second = 1 Hertz (Hz) = 1 /s unit of frequency Eg. Vibrating electrons are the source of radio waves Electrons in this antenna vibrate 940 000 times per second – ie at 940 kHz. This is the freq of the radio waves produced. AM radio waves are in kilohertz (kHz =1000Hz), while FM are in megahertz (MHz = 10 6 Hz). Microwaves oscillate at
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Lec15 - Today Chapter 19(Vibrations and Waves Vibrations...

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