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Lecture 2

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SCI 206
Stefan Idziak

Resonance 1 Waves  What is a pulse on a string? Describe some characteristics of it. o It is a "bump" that travels along a string o It has a defined direction and has the ability to be reflected off the ends of the string o It does not cause the string itself to move - it only causes sections of the string to be displaced vertically  What is a transverse wave? Identify the following features of a transverse wave: amplitude, node, antinode, velocity, and wavelength. o A transverse wave is one where the displacement created is vertical  If we have a transverse wave on a string, what force causes the vertically-displaced portions of the string to oscillate "up and down"? o The tension on the string acts as a restoring force to bring it back to the middle, but it overshoots and goes to a maximum amplitude on the other side  Explain how longitudinal waves work. o Longitudinal waves are those where the displacement is longitudinal - i.e. along the length of the wave  It is a series of compressions and stretches (aka rarefactions)  Discuss how sound is a longitudinal wave. What implications does this have for the necessary conditions for hearing sound? o Sound waves are simply longitudinal waves in air - and the analog of "compressions" and "rarefactions" are regions of high and low air pressure o The implication is that we must have air in order to hear sound - because to hear sound is simply for our ear to detect the pattern of air pressure changes  Recall the demo where a bell in a vacuum was rung, and no sound was heard  How are the speed, frequency, and wavelength of a wave related? What implication does this have for sound in different mediums? o Speed = frequency x wavelength o The implication is that sound travels at different speeds in different mediums, and so when sound passes from one medium to another, the speed will change: thus either frequency or wavelength must change  Frequency does NOT change, and so wavelength does - thus the sound we hear is different  Give an example of a wave traveling through different mediums. o If we pluck a guitar string, first the string vibrates in the form of a characteristic wave, and then it causes the air around it to vibrate - and we hear that in our ear Doppler Effect  Explain what the Doppler Effect is. Give an example. o It is the phenomenon where a sound will sound different if its source is traveling either toward you or away from you than it would if the source was stationary o This is why the siren from a police car or fire truck will appear to change in tone if you are standing on the side of the road and the car comes towards you, passes you, and continues on away from you Resonance 2  How does the Doppler Effect work? o It is because the sound waves are either compressed (coming towards you) or expanded (going away from you), and thus the altered wavelengths are perceived differently  How do sonic booms work? o This is an extreme application of the Doppler Effect whereby the source of sound created is so loud that the waves are compressed so much that they all arrive at essentially the same time at a single spot, and an extremely loud sound is created Oscillations & Resonance  Explain how a pendulum is an example of a simple harmonic oscillator. o It is because if we pull the mass to the left or right then let go, the tension in the string will cause the mass to swing back in the direction of the equilibrium position, and in fact surpass it and go to an extreme on the other side o The force that does this (and is definitive of simple harmonic oscillation) is a "restoring force": a restoring force always tries to bring the mass to equilibrium  Discuss the relationship which the restoring force has to the object's distance from the equilibrium point. What implication does this have for the period of a given pendulum? o The restoring force is linearly proportional to the object's distance from equilibrium: the further away the object is, the stronger the force is which wants the object to return  It consists of the force created by the tension of the string and gravity o The implication is that for a given pendulum, its period will always be the same…  Regardless of how far away you initially bring the pendulum  And also regardless of what the MASS of the swinging object is o The ONLY FACTOR that can change the pendulum's period is the length of the string  Explain how pendulum clocks work. o There is a circle with 30 teeth (a gear), and an apparatus attached to a pendulum o The apparatus is positioned such that every time the pendulum completes an oscillation (period = 2 seconds), the apparatus clicks past one "tooth" o Thus, every time the gear completes a full revolution, we know that it has been one minute (60 seconds)  Describe the motion of a mass on a spring, and why it is a harmonic oscillator. o Firstly, there is an equilibrium point - where the spring is neither stretched nor compressed o If we (for instance) pull the mass such that we are not at the equilibrium point and the spring is stretched, we will feel tension because the restoring force in the spring wants to return the mass to the equilibrium point o It is a harmonic oscillator because if we release the mass, it will accelerate back towards the equilibrium position and overshoot it to the other side, compressing the spring and creating another restoring force that pushes the mass again back to the equilibrium position from the other side  How do we adjust
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