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# Lect02 - Lecture 2 Interference l d S1 S2 Interference of...

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Lecture 2, p.1 Lecture 2: Interference S 1 S 2 d l Interference of sound waves Two-Slit Interference Phasors

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The Many “Fathers” of QM 1900 Planck “solves” the blackbody problem by postulating that the oscillators in the walls have quantized energy levels. “Until after some weeks of the most strenuous work of my life, light came into the darkness, and a new undreamed-of perspective opened up before me…the whole procedure was an act of despair because a theoretical interpretation had to be found at any price, no matter how high that might be.” 1905 Einstein proposes that light energy is quantized ”photons” 1913 Bohr proposes that electron orbits are quantized 1923 de Broglie proposes that particles behave like waves 1925 Pauli introduces “exclusion principle” – only 2 electrons/orbital 1925 Heisenberg introduces matrix-formulation of QM 1926 Schrödinger introduces the wave-formulation of QM
Lecture 2, p.3 Adding Sine Waves with Different Phases Suppose we have two sinusoidal waves with the same A 1 , , and k : y 1 = A 1 cos(kx - t) and y 2 = A 1 cos(kx - t + ) One starts at phase after the other:   11 cos cos 2 cos cos 22 AA    12 yy   /2   kx t  1 2 cos( /2) cos( /2) y A kx t Use this trig identity: Spatial dependence of 2 waves at t = 0: Resultant wave: Amplitude Oscillation y = y 1 +y 2

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Lecture 2, p.4 ACT 1: Noise-cancelling Headphones 1. What must be the phase of the signal from the speaker relative to the external noise? a. 0 b. 90˚ c. p d. -180˚ e. 2 p 2. What must be the intensity I s of the signal from the speaker relative to the external noise I n ? a. I s = I n b. I s < I n c. I s > I n Noise-canceling headphones work using interference. A microphone on the earpiece monitors the instantaneous amplitude of the external sound wave, and a speaker on the inside of the earpiece produces a sound wave to cancel it.
Lecture 2, p.5 Solution Destructive interference occurs when the waves are ±180˚ out of phase. 180º = p radians! 1. What must be the phase of the signal from the speaker relative to the external noise? a. 0 b. 90˚ c. p d. -180˚ e. 2 p 2. What must be the intensity I s of the signal from the speaker relative to the external noise I n ? a. I s = I n b. I s < I n c. I s > I n Noise-canceling headphones work using interference. A microphone on the earpiece monitors the instantaneous amplitude of the external sound wave, and a speaker on the inside of the earpiece produces a sound wave to cancel it.

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Lecture 2, p.6 We want A = A s -A n = 0. Note that I is never negative. Solution 1. What must be the phase of the signal from the speaker relative to the external noise? a. 0 b. 90˚ c. p d. -180˚ e. 2 p 2. What must be the intensity I s of the signal from the speaker relative to the external noise I n ?
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Lect02 - Lecture 2 Interference l d S1 S2 Interference of...

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