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Lecture 28

# Lecture 28 - Lecture 28 Final Exam Review Final Exam o The...

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Lecture 28 Final Exam Review

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Final Exam o The final exam will be on Wed June 11 from 10:30am-12:30pm in this room. o Exam will consist of 10 multiple choice questions and 3 long answer questions + 3 short answer questions. o ~1/3 material from *previous material* + 2/3 material covered since the midterm.
Hooke’s Law and Springs Equilibrium Remember that a block on a spring oscillates in time like a cosine wave because springs pull and push against displacement as: F=-kx

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Understanding wave functions o A spring is oscillating at an angular fequency of pi radians per second. It is observed to peak after 1.5 second. What is the phase constant? time t X position φ 0
A is the amplitude, ω is the angular frequency, and φ is the “phase”. The value of φ is set by the time when x reaches its peak value. The frequency f and period T are related to ω as For the special case of a block on a spring : ω is related to the spring constant and mass via: and the energy of the system is described by: Oscillators - Bock & Spring The position, velocity, and acceleration of an object in simple harmonic motion can be described as:

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Traveling Sinusoidal wave function Travels to the right at speed v
Transverse Velocity vs. Wave Velocity o The general solution for a sinusoidal wave allows us to calculate the transverse (up and down) velocity and acceleration at any point and time:

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Travels to the right at speed v Travels to the left at speed v. Review Transverse velocity / acceleration. Speed of traveling wave on string density μ tension T: Power transmitted:
String with ends pegged

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Harmonics: string with ends pegged o There are an infinite number of harmonics, with the nodes spaced closer and closer as n increases o In general for the n’th harmonic: L = n λ n /2 , or λ n = 2L/n o Drawing a picture helps a lot!

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Phase difference Example Problem: o Two sound waves with identical wavelengths of 1.5 m
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