波和量子物理-資料下載頁
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【正文】 2co s2co sA2co sco sA 1121 yy ? ? ?2/?? ?2/tkx ????)2/tkxco s ( )2/co s (A2 y 1 ??????Trig identity: y1 = A1 cos(k x ? t) and y2 = A1 cos(k x ? t + ?) Spatial dependence of 2 waves at t = 0: Resultant wave: Amplitude Oscillation y = y1 +y2 ? Interference of Waves ? What happens when waves from two sources arrive at the same point in space and time? (single ? case) ? Always add amplitudes (pressures or electric fields). ? What we observe however is Intensity (absorbed power). I = A2 Stereo speakers: Listener: 1F o r 2 e q u a l w a v e s , A 2 A c o s ( / 2 ) ??Example: ? “ Constructive interference”: waves are “in phase” (? = 0, 2?, 4?, ..) ? “Destructive interference”: waves are “out of phase” (? = ?, 3?, 5?, …) Of course, ? can take on an infinite number of values. We won’t use terms like “mostly constructive” or “slightly destructive”. Terminology Act 5: Changing phase of the Source Each speaker alone produces an intensity of I1 = 1 W/m2 at the listener: Drive the speakers in phase. What is the intensity I at the listener? Now shift phase of one speaker by is the intensity I at the listener? ? I = I1 = 1 W/m2 I = I = Act 5: Solution Each speaker alone produces an intensity of I1 = 1 W/m2 at the listener: Drive the speakers in phase. What is the intensity I at the listener? Now shift phase of one speaker by is the intensity I at the listener? ? I = A12 = I1 = 1 W/m2 I = I = Act 5: Solution Each speaker alone produces an intensity of I1 = 1 W/m2 at the listener: Drive the speakers in phase. What is the intensity I at the listener? Now shift phase of one speaker by is the intensity I at the listener? ? I = A12 = I1 = 1 W/m2 I = (2A1)2 = 4I1 = 4 W/m2 I = Act 5: Solution Each speaker alone produces an intensity of I1 = 1 W/m2 at the listener: Drive the speakers in phase. What is the intensity I at the listener? Now shift phase of one speaker by is the intensity I at the listener? ? I = A12 = I1 = 1 W/m2 I = (2A1)2 = 4I1 = 4 W/m2 I = 4 I1cos2(450) = I1 = W/m2 Problem for next time: path lengthdependent phase Each speaker alone produces intensity I1 = 1W/m2 at the listener, and f = 900 Hz. Drive speakers in phase. Compute the intensity I at the listener in this case: I = I1 = 1 W/m2 r1 = 4 m Sound velocity: v = 330 m/s Check your solution next lecture. Hint: ? ? 2??d/?? with d ? r2 r1 Do you see why? r1 A1 = ? I1 Procedure: 1) Compute pathlength difference: d = 2) Compute wavelength: ? = 3) Compute phase difference: ? ? 4) Write formula for resultant amplitude A = 5) Compute the resultant intensity, I = A2 = Answer: I = ?? W/m2 Home Exercise 1: ? Assume two waves with the same amplitude A1 = 1 cm and angular frequency ?. They differ only in phase ? : ? The resultant wave is: y1 = A1cos(k x ? t) and y2 = A1cos(k x ? t + ?) ? Determine the amplitude A of the resultant wave in the following cases (you plete the table): ? (degrees) ? (radians) A (cm) Rough Drawing 450 ?/4 900 1800 3600 300 )2/co s (2A A w i t h)2/tkxco s ( A y y y 121 ????????? Wele to Physics 214 ? Content: Waves and Quantum Physics ?Format: Active Learning (Learn from Participation) ?Textbook – Young and Freedman Assignments on Syllabus page ? Lectures (presentations, demonstrations, amp。 ACTs) ? Discussion Sections (group problem solving) start this week ? Labs (handson interactions with the phenomena) Submit Prelab to instructor at 1st session Bring your calculator! Ask the Professor (from the Homepage): An opportunity for you to get answers in lecture to your questions. This Thursday only: 2 bonus points for filling in the “Ask the Professor” survey. James Scholar Students: Email me within 1 week. w01
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