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====== Differences ====== This shows you the differences between two versions of the page.
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draft_page_2 [2014/04/17 22:53] veckert [Problem 54 part B] |
draft_page_2 [2014/05/18 22:33] (current) 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? | ||
| Line 39: | Line 75: | ||
| Sound Propagation Problem: | Sound Propagation Problem: | ||
| - | Peak Blood Velocity in a fetal aorta is about 20cm/s. If we image it a 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) | ||
draft_page_2.1397775223.txt.gz · Last modified: 2014/04/17 22:53 by veckert
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