# Lect03 - Review Examples and Phasors Examples A1 d S2...

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

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Review: The Harmonic Waveform () ( ) ( ) 2 ,c o s c o s 2 c o s s the displacement from equilibrium yx t A x v t A k x f t A k x t π ω λ =− ⎛⎞ ⎜⎟ ⎝⎠ speed amplitude (defined to be positive) 2 wavelength wavenumber is the displacement from equilibrium. vA k y ≡≡ A function of two variables: x and t . frequency 2 angul frequency ar f f A snapshot of y( x ) at a fixed time, t : λ Wavelength Amplitude A v defined to be positive A x Lecture 3, p 2 This is review from Physics 211/212. For more detail see Lectures 26 and 27 on the 211 website.
Review: Adding Sine Waves Suppose we have two sinusoidal waves with the same A 1 , ω , and k . Suppose one starts at phase φ after the other: A os(kx nd A os(kx + y 1 = A 1 cos(kx - ω t) and y 2 = A 1 cos(kx - ω t + φ ) Spatial dependence φ of 2 waves at t = 0: Resultant wave: y = y 1 +y 2 ( ) 1 cos cos 2 cos cos AA β αβ α −+ ⎛⎞ + = ⎜⎟ Use this trig identity: 11 22 ⎝⎠ 12 y y + ( ) / 2 φ ( ) / 2 kx t ωφ Lecture 3, p 3 1 2 cos( /2) cos( /2) yA k x t = Amplitude Oscillation

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Example: Changing phase of the Source Each speaker alone produces an intensity of I 1 = 1 W/m 2 at the listener: I = I 1 = A 1 2 = 1 W/m 2 Drive the speakers in phase. What is the intensity I at the listener? I = Now shift phase of one speaker by 90 o .What is the intensity I at the listener? o s p ase o o e spea e by 90 as e esya esee = Lecture 3, p 4 φ I =
Example: Changing phase of the Source Each speaker alone produces an intensity of I 1 = 1 W/m 2 at the listener: I = I 1 = A 1 2 = 1 W/m 2 Drive the speakers in phase. What is the intensity I at the listener?

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Lect03 - Review Examples and Phasors Examples A1 d S2...

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