# Physics 203 at Portland State 2014

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draft_page_2 [2014/04/17 22:53]
veckert [Problem 54 part B]
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tom_grass [Practice/work here if other pages are temporarily locked by other editors]
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+====Equation Sheet Ch.28====
+
+28-1:  Conditions for Bright Fringes (Constructive Interference) In a Two Slit Experiment:  ​
+    *$d sin θ = m\lambda$. ​ $d$ is the slit separation
+    *$m=0,​±1,​±2,​±3.,​..$
+    *$m=0$ occurs at $θ=0$, this is the central bright fringe. ​
+    *Positive values of $m$ are above the central bright fringe, negative values are below. ​
+    *Solving for $θ: θ = sin^{-1} (m\frac{\lambda}{d})$
+
+28-2:  Conditions for Dark Fringes (Destructive Interference) in a Two Slit Experiment:  ​
+      * $d sin θ = (m-\frac{1}{2})\lambda.$ ​ $m = 1,2,3...$ (above central bright fringe)
+      * $d sin θ = (m+\frac{1}{2})\lambda.$ ​ $m = -1,​-2,​-3...$ (below central bright fringe)
+      * Solving for $θ: θ = sin^{-1} [(m ± \frac{1}{2})\frac{\lambda}{d}]$. ​ $+ or -$ depending on location. ​
+
+28-3  Linear Distance from Central Fringe:  ​
+        * $y = L tan θ$.  L is the distance to the screen. ​
+        * Solving for $θ$ of a bright fringe: ​ $θ = tan^{-1} (m\frac{y}{L})$
+        * Solving for $\lambda: ​ \lambda = \frac{d}{m}sinθ$
+        * Solving for $θ$ of a dark fringe: ​ $θ = sin^{-1}[(m±\frac{1}{2})\lambda/​d]$. ​ $+ or -$ depending on location.
+
+28-12  Conditions for Dark Fringes in Single-Slit Interference:  ​
+       * $Wsin θ = m\lambda$. ​  $m = ±1,​±2,​±3...$
+       * Solving for $\lambda: \lambda = \frac{Wsinθ}{m}$ \
+       * Solving for $θ: θ = sin^{-1}(\frac{m\lambda}{W})$
+
+28-14  First Dark Fringe for the Diffraction Pattern of a Circular Opening:  ​
+      * $sinθ = 1.22\frac{\lambda}{D}$
+
+28-15  Rayleigh'​s Criterion:
+     * $θ_{min} = 1.22\frac{\lambda}{D}$
+     * Note: $\lambda$ is dependent on the diffraction of the material that the light is traveling through. ​ If the diffraction is $n, \lambda$ becomes $\frac{\lambda}{n}$
+
+28-16: ​ Constructive Interference in a Diffraction Grating:  ​
+     * $d sin θ = m\lambda$. ​   $m = ±1,​±2,​±3...$
+     * Solving for $d: d = \frac{m\lambda}{sinθ}$
+
===Problem 1.3.13.13=== ===Problem 1.3.13.13===
Two pendulums (or, //​pendula//​) are made of identical 1 kg masses suspended on two weightless strings, 40.0 and 40.5 cm in length. If these pendulums are deflected from vertical by 5 cm and released at the same time, how long will it take for them to get completely "out of step" with each other? Two pendulums (or, //​pendula//​) are made of identical 1 kg masses suspended on two weightless strings, 40.0 and 40.5 cm in length. If these pendulums are deflected from vertical by 5 cm and released at the same time, how long will it take for them to get completely "out of step" with each other?
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Sound Propagation Problem: Sound Propagation Problem:

-Peak Blood Velocity in a fetal aorta is about 20cm/s. If we image it 9MHz, find the Doppler shift.+Peak Blood Velocity in a fetal aorta is about 20cm/s. If we image it at 9MHz, find the Doppler shift.
V=1500m/s V=1500m/s
f=(1+(Vobserver/​V))/​(1-(Vsource/​V) ​ f=(1+(Vobserver/​V))/​(1-(Vsource/​V) ​ 