# Lect03 - Le cture3: Re w, Exam s and Phasors vie ple A A S1...

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Lecture 3, p 1 Lecture 3: Review, Examples and Phasors S 1 S 2 d λ A 1 A 1 A φ = 45 ° 8 / λ δ=

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Lecture 3, p 2 Review: The Harmonic Waveform ( 29 ( 29 ( 29 ( 29 speed amplitude (defined to be positive) 2 wavelength wavenumber frequency 2 , cos 2 angul frequency ar cos 2 cos is the displacement from equilibrium. y x t A x vt A kx ft A kx t v A k f f y π λ ϖ = - - - A snapshot of y( x ) at a fixed time, t : This is review from Physics 211/212. For more detail see Lectures 26 and 27 on the 211 website. λ Wavelength Amplitude A defined to be positive A x v A function of two variables: x and t .
Lecture 3, p 3 Review: Adding Sine Waves Suppose we have two sinusoidal waves with the same A 1 , ϖ , and k . Suppose one starts at phase φ after the other: ( 29 1 1 cos cos 2 cos cos 2 2 A A β α - + + = 1 2 y y + ( 29 / 2 φ ( 29 / 2 kx t ϖ - + 1 2 cos( /2) cos( / 2) y A kx t = - + Use this trig identity: y 1 = A 1 cos(kx - ϖ t) and y 2 = A 1 cos(kx - ϖ t + φ ) Spatial dependence of 2 waves at t = 0: Resultant wave: Amplitude Oscillation y = y 1 +y 2 φ

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Lecture 3, p 4 Example: Changing phase of the Source Each speaker alone produces an intensity of I 1 = 1 W/m 2 at the listener: Drive the speakers in phase. What is the intensity I at the listener? Now shift phase of one speaker by 90 o .What is the intensity I at the listener?
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## Lect03 - Le cture3: Re w, Exam s and Phasors vie ple A A S1...

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