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exam_2_review [2014/05/10 02:04]
wikimanager [All of the parameters for each wave are summarized below]
exam_2_review [2014/05/14 14:48] (current)
wikimanager [Review problem 3] added solution
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 ====Review question 1==== ====Review question 1====
 The focal lengths of the objective and the eyepiece in a microscope are 0.29 cm and 2.5 cm, respectively. An object is placed 0.3 cm from the objective. The image of this object is viewed with the eyepiece adjusted for minimum eyestrain. What is the distance between the objective and the eyepiece? ​ The focal lengths of the objective and the eyepiece in a microscope are 0.29 cm and 2.5 cm, respectively. An object is placed 0.3 cm from the objective. The image of this object is viewed with the eyepiece adjusted for minimum eyestrain. What is the distance between the objective and the eyepiece? ​
-    * [....] A) 11.2 cm +    * [ <color green>​X</​color> ​] A) 11.2 cm 
     * [....] B) 10.1 cm      * [....] B) 10.1 cm 
     * [....] C) 10.4 cm      * [....] C) 10.4 cm 
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 ====Review question 2==== ====Review question 2====
 A magnifying glass uses a converging lens with a refractive power of 20 diopters. What is the magnification if the image is to be viewed by a relaxed eye with a near point of 25 cm?  A magnifying glass uses a converging lens with a refractive power of 20 diopters. What is the magnification if the image is to be viewed by a relaxed eye with a near point of 25 cm? 
-  * [....] A) 5.0+  * [ <color green>​X</​color> ​] A) 5.0
   * [....] B) 4.0   * [....] B) 4.0
   * [....] C) 1.0   * [....] C) 1.0
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   * [....] C) $+2.5$ diopters ​   * [....] C) $+2.5$ diopters ​
   * [....] D) $+2.7$ diopters ​   * [....] D) $+2.7$ diopters ​
-  * [....] E) $-2.5$ diopters ​+  * [ <color green>​X</​color> ​] E) $-2.5$ diopters ​
  
 <color green></​color>​ <color green></​color>​
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   * [....] A) Convex. ​   * [....] A) Convex. ​
   * [....] B) Plane. ​   * [....] B) Plane. ​
-  * [....] C) Concave. ​+  * [ <color green>​X</​color> ​] C) Concave. ​
   * [....] D) All of the given answers would work equally as well.    * [....] D) All of the given answers would work equally as well. 
   * [....] E) None of the given answers would burn a hole.    * [....] E) None of the given answers would burn a hole. 
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 You have a choice between two lenses of focal lengths $f_a$ and $f_b = 2 f_a$ to use as objective lens in building a compound microscope. If the magnification you obtain using lens //a// is $M_a$, what will be the magnification when using lens //​b//? ​ You have a choice between two lenses of focal lengths $f_a$ and $f_b = 2 f_a$ to use as objective lens in building a compound microscope. If the magnification you obtain using lens //a// is $M_a$, what will be the magnification when using lens //​b//? ​
   * [....] A) $M_b = \frac{1}{4} M_a$   * [....] A) $M_b = \frac{1}{4} M_a$
-  * [....] B) $M_b = \frac{1}{2} M_a$+  * [ <color green>​X</​color> ​] B) $M_b = \frac{1}{2} M_a$
   * [....] C) $M_b = 8 M_a$   * [....] C) $M_b = 8 M_a$
   * [....] D) $M_b = 4 M_a$    * [....] D) $M_b = 4 M_a$ 
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 Which of the following expressions is correct for the transmitted intensity of an unpolarized beam of light with an intensity $I_i$ passing through a polarizer? ​ Which of the following expressions is correct for the transmitted intensity of an unpolarized beam of light with an intensity $I_i$ passing through a polarizer? ​
   * [....] A) $I_t = 2 I_i$   * [....] A) $I_t = 2 I_i$
-  * [....] B) $I_t = \frac{1}{2} I_i$+  * [ <color green>​X</​color> ​] B) $I_t = \frac{1}{2} I_i$
   * [....] C) $I_t = I_i$   * [....] C) $I_t = I_i$
   * [....] D) $I_t = 4 I_i$   * [....] D) $I_t = 4 I_i$
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   * [....] A) neither spherical nor chromatic aberration. ​   * [....] A) neither spherical nor chromatic aberration. ​
   * [....] B) chromatic aberration, but not spherical aberration. ​   * [....] B) chromatic aberration, but not spherical aberration. ​
-  * [....] C) spherical aberration, but not chromatic aberration.+  * [ <color green>​X</​color> ​] C) spherical aberration, but not chromatic aberration.
   * [....] D) both spherical and chromatic aberration. ​   * [....] D) both spherical and chromatic aberration. ​
  
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   * [....] B) $4.8$ m    * [....] B) $4.8$ m 
   * [....] C) $4.2$ m    * [....] C) $4.2$ m 
-  * [....] D) $-4.2$ m +  * [ <color green>​X</​color> ​] D) $-4.2$ m 
   * [....] E) $5.2$ m    * [....] E) $5.2$ m 
  
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   * [....] B) $-36.4$ cm   * [....] B) $-36.4$ cm
   * [....] C) $-21.2$ cm   * [....] C) $-21.2$ cm
-  * [....] D) $+36.4$ cm+  * [ <color green>​X</​color> ​] D) $+36.4$ cm
   * [....] E) $+21.2$ cm   * [....] E) $+21.2$ cm
  
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- 
 ====Review question 10==== ====Review question 10====
 An object is placed in front of a convex mirror at a distance larger than twice the focal length of the mirror. The image will appear ​ An object is placed in front of a convex mirror at a distance larger than twice the focal length of the mirror. The image will appear ​
   * [....] A) upright and enlarged.  ​   * [....] A) upright and enlarged.  ​
-  * [....] B) upright and reduced.+  * [ <color green>​X</​color> ​] B) upright and reduced.
   * [....] C) inverted and enlarged.   * [....] C) inverted and enlarged.
   * [....] D) inverted and reduced.  ​   * [....] D) inverted and reduced.  ​
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   * [....] A) 2.0    * [....] A) 2.0 
   * [....] B) 1.5    * [....] B) 1.5 
-  * [....] C) 1.0 +  * [ <color green>​X</​color> ​] C) 1.0 
   * [....] D) 0.25   * [....] D) 0.25
   * [....] E) 0.5    * [....] E) 0.5 
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 ====Review question 12==== ====Review question 12====
 A vertically polarized beam of light of intensity $100\frac{\text W}{\,{\text m}^2}$ passes through a polarizer with its transmission axis at 40.0$^\circ$ to the vertical. What is the transmitted intensity of this beam of light? ​ A vertically polarized beam of light of intensity $100\frac{\text W}{\,{\text m}^2}$ passes through a polarizer with its transmission axis at 40.0$^\circ$ to the vertical. What is the transmitted intensity of this beam of light? ​
-  * [....] A) $58.7\frac{\text W}{\,{\text m}^2}$ ​+  * [ <color green>​X</​color> ​] A) $58.7\frac{\text W}{\,{\text m}^2}$ ​
   * [....] B) $0\frac{\text W}{\,{\text m}^2}$ ​   * [....] B) $0\frac{\text W}{\,{\text m}^2}$ ​
   * [....] C) $100\frac{\text W}{\,{\text m}^2}$ ​   * [....] C) $100\frac{\text W}{\,{\text m}^2}$ ​
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   * [....] A) 200 cm    * [....] A) 200 cm 
   * [....] B) 101 cm    * [....] B) 101 cm 
-  * [....] C) 198 cm +  * [ <color green>​X</​color> ​] C) 198 cm 
   * [....] D) 202 cm    * [....] D) 202 cm 
   * [....] E) 2.0 cm   * [....] E) 2.0 cm
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   * [....] C) half as large as his face    * [....] C) half as large as his face 
   * [....] D) four times as large as his face    * [....] D) four times as large as his face 
-  * [....] E) three times as large as his face+  * [ <color green>​X</​color> ​] E) three times as large as his face
  
 <color green></​color>​ <color green></​color>​
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   * [....] B) a short focal length objective and a long focal length eyepiece.   * [....] B) a short focal length objective and a long focal length eyepiece.
   * [....] C) a short focal length objective and a short focal length eyepiece. ​   * [....] C) a short focal length objective and a short focal length eyepiece. ​
-  * [....] D) a long focal length objective and a short focal length eyepiece.+  * [ <color green>​X</​color> ​] D) a long focal length objective and a short focal length eyepiece.
  
 <color green></​color> ​ <color green></​color> ​
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 ====Review problem 2==== ====Review problem 2====
-{{ :​figs:​ex1rev2.jpg?​nolink&​189|}} ​musician (Andrew Bird) used double spinning horn speaker during ​recent tourWhile one horn spins toward you, the other spins awaySay the horns are emitting a frequency ​of 880 Hz, are spinning with an angular velocity ​of 2.0 rad/s, and that each horn is 1.0 m long.  +meter stick lies along the principal axis of convex mirror with focal length of 30.0 cm. Two 10.0 cm toy figures ​are placed upright on near and far end of the meter stick. The closer ​of the two figures ​is 50.0 cm away from the mirror 
-  * a) Due to a Doppler shift, what is the greatest pitch (frequency $f$) you will hear? Will this be when the horn is spinning towards you or away from you? (Remember, $v_t = A\omega$, where $A$ is the distance from the rotation axis to the opening of the horn) (pts) +{{ :​figs:​ex2rev2.png?​nolink| }} 
-    * <color green>Greatest pitch - motion towards you</​color>​ + 
-    * <color green>$f'​=f\left(\frac{1}{1-\frac{u}{v}}\right)$ $=f\left(\frac{1}{1-\frac{A\omega}{v}}\right)$ $=880\,​{\text{Hz}}\,​\left(\frac{1}{1-\frac{1.0\,{\text m}\,​\cdot\,​2.0\,​\frac{\text{rad}}{\text s}}{340\,​\frac{\text m}{\text s}}}\right)$ $=885\,​$Hz  ​</​color>​ +  * a) How far away from the mirror ​is the image of the figure that is closest ​to the mirror? ​(pts) 
-  * b) What is the lowest pitch you will hear from the speakers due to a Doppler shift? Will this be when the horn is spinning towards you or away from you? (pts) +    * <color green>...</​color>​ 
-    * <color green>Lowest pitch - motion away from you</​color>​ +      * <color green>...</​color>​ 
-    * <color green>$f'​=f\left(\frac{1}{1+\frac{u}{v}}\right)$ $=f\left(\frac{1}{1+\frac{A\omega}{v}}\right)$ $=880\,​{\text{Hz}}\,​\left(\frac{1}{1+\frac{1.0\,{\text m}\,​\cdot\,​2.0\,​\frac{\text{rad}}{\text s}}{340\,​\frac{\text m}{\text s}}}\right)$ $=875\,​$Hz  ​</​color>​ +  * b) How far away from the mirror ​is the image of the figure that is furthest ​from the mirror? (pts) 
-  * c) What is the beat frequency you hear from this instrument? (pts) +    * <color green>...</​color>​ 
-    * <color green> ​$f_\text{beat}=\big|\,​f_1-f_2\big|$ $=\big|885\,​{\text{Hz}}-875\,​{\text{Hz}}\big|$ $=10\,​$Hz ​  </​color>​ +      * <color green>...</​color>​ 
-  * d) At the concert your friend sitting 1 m from the speakers hears an intensity ​of $9.0\times 10^{-2}\frac{\text W}{\,{\text m}^2}$. What intensity do you hear sitting 10 m away from the speakers? (pts) +  * c) What is the length of the image of the meter stick? (in other words, what is the distance between the two images of the figures?) (1 pts) 
-    * <color green> ​$I=\frac{\text{Power}}{4\pi r^2}$   </​color>​ +    * <color green>...</​color>​ 
-    * <color green> ​$\frac{I_\text{friend}}{I_\text{you}}=\frac{(10\,​{\text m})^2}{(1\,​{\text m})^2}$ $=100$ ​   </​color>​ +  * d) How tall is the closer ​of the two figures to the mirror in the image? (pts) Is it upright or inverted? (1 pt
-    * <color green> $I_\text{you}=\frac{1}{100}I_\text{friend}$ $=9.0\times 10^{-4}\frac{\text W}{\,{\text m}^2}$ ​  </​color>​ +    * <color green>...</​color>​ 
-  * e) What is the intensity level in decibels that your friend hears? (pts) +      * <color green>...</​color>​ 
-    * <color green> ​$\beta=10\,​{\text{dB}}\log\left(\frac{I_1}{I_\text{t.h.}}\right)$ $=10\,​{\text{dB}}\log\left(\!\frac{9.0\times 10^{-2}\frac{\text W}{\,{\text m}^2}}{ 10^{-12}\frac{\text W}{\,{\text m}^2}}\!\right)$ $\approx 110\,​$dB  ​</​color>​+  * e) How tall is the farther of the two figures from the mirror ​in the image? (pts) Is it upright or inverted? (1 pt)  
 +    * <color green>​...</​color>​
  
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 ====Review problem 3==== ====Review problem 3====
 Match the definitions and descriptions with the best term or phrase given below (1.5 pts each): Match the definitions and descriptions with the best term or phrase given below (1.5 pts each):
- ​Resonance ​\\ Underdamping ​\\ Critical damping ​\\ Overdamping ​\\ Period ​\\ Frequency ​\\ Angular frequency ​\\ Wavelength ​\\ Simple pendulum ​\\ Physical pendulum ​\\ Transverse wave \\ Longitudinal wave  ​\\ Linear mass density ​  |  ​Wave function ​\\ Reflections ​\\ Ultrasound ​\\ Intensity ​\\ Decibel ​\\ Doppler effect ​\\ Superposition ​\\ Constructive interference ​\\ Destructive interference ​\\ Standing wave \\ Fundamental frequency ​\\ 2<​sup>​nd</​sup>​ Harmonic frequency ​\\ 3<​sup>​rd</​sup>​ Harmonic frequency  ​ Beat frequency ​\\ In-phase sources ​\\ Opposite phase sources ​\\ Direction of propagation of light \\ Speed of light in a vacuum ​\\ Microwaves ​\\ Radio waves \\ Infrared ​\\ Visible ​\\ Ultraviolet ​\\ x-rays ​\\ Gamma rays  ​|+  polarizer’s transmission axis \\ polarization ​\\ rays \\ wave fronts ​\\ specular reflection ​\\ diffuse reflection ​\\ focal point \\ index of refraction ​\\ total internal reflection ​\\ Snell'​s law \\ sign conventions ​\\ incident angle \\ angle of reflection \\ angle of refraction ​  |  ​focal length ​\\ magnification ​\\ image distance ​\\ object distance ​\\ real object ​\\ virtual object ​\\ real image \\ virtual image \\ concave mirror ​\\ convex mirror ​\\ converging lens \\ diverging lens \\ Brewster'​s angle \\ critical angle     nearsighted ​\\ farsighted ​\\ refractive power \\ diopter ​\\ far point \\ near point \\ magnifying lens \\ telescope ​\\ compound microscope ​\\ aberration ​\\ spherical aberration ​\\ chromatic aberration \\ dispersion \\ rainbow ​  |
  
-  - Two sources that emit crests at the same time and emit troughs at the same time+  - A lens with a negative focal length
-    * <color green>In-phase sources</​color>​  +    * <color green>diverging lens</​color>​  
-  - Ninety degrees to both the electric field and the magnetic field in a moving electromagnetic wave.  +  - A problem ​in lenses where different colors of light are focused to different focal points.  
-    * <color green>Direction of propagation of light</​color>​  +    * <color green>chromatic aberration</​color>​  
-  - Energy per unit time per unit area+  - The angle of incidence of light such that after striking a surface the reflected light is completely polarized
-    * <color green>Intensity</​color>​  +    * <color green>Brewster'​s angle</​color>​  
-  - A measure of sound intensity. Increasing by about three of these units will indicate ​doubling ​of the intensity of the sound+  - Reflection from rough surface such that light is sent out in a variety ​of directions
-    * <color green>Decibel</​color>​  +    * <color green>diffuse reflection</​color>​  
-  - When two waves combine to create a wave with an amplitude less than either ​of the two original waves+  - Light rays converge towards this type of object. The sign convention for the distance to the object in this case is negative
-    * <color green>Destructive interference</​color>​  +    * <color green>virtual object</​color>​  
-  - A part of the electromagnetic spectrum with frequencies just greater than those visible by humans. +  - The ability ​of a lens to refract light (commonly measured in diopters) 
-    * <color green>Ultraviolet</​color>​  +    * <color green>refractive power</​color>​  
-  - A point mass on the end of a mass-less string that is allowed ​to swing back and forth+  - A problem in lenses and mirrors ​of a particular shape where light further away from the principal axis is focused ​to a different point than light closer to the principal axis
-    * <color green>Simple pendulum</​color>​  +    * <color green>spherical aberration</​color>​  
-  - A wave where the direction ​of the molecules ​is perpendicular to the direction ​of the wave. +  - The length ​of this device ​is the sum of the two focal lengths of the lenses used to make it 
-    * <color green>Transverse wave</​color>​  +    * <color green>telescope</​color>​  
-  - The lowest frequency that can be created on string or in a tube. +  - A property of material that is related to how fast light travels ​in the material 
-    * <color green>Fundamental frequency</​color>​  +    * <color green>index of refraction</​color>​  
-  - The length ​of time between two wave crests+  - Colorful object seen in the sky due to the dispersion ​of light in raindrops
-    * <color green>Period</​color> ​+    * <color green>rainbow</​color> ​
  
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-{{ :​figs:​ex1rev3.jpg?​292|}} 
 ====Review problem 4==== ====Review problem 4====
-The air pressure variations in a sound wave cause the eardrum ​(tympanic membrane to vibrate+While wandering on Mars (which has little atmosphere and can be considered a vacuum environment), you stumble upon a mysterious cube of an unknown material. You have a red and a blue laser handy and perform a few experiments. You observe that total internal reflection occurs at the critical angle of 19.5$^\circ$ for red light
-  - For given vibration amplitude, are the maximum velocity and acceleration ​of the eardrum greatest for high frequency sounds or low frequency sounds? (1 pts+  - To observe total internal reflection did you scrutinize ​ray of light going from the mystery material to vacuum or a ray of light going from vacuum to the mystery material ( 1 pt
-    * <color green>$v_\text{max}$ $=x_\text{max}\omega$</​color>​ +    * <color green>...</​color>​ 
-    * <color green>​$a_\text{max}$ $=x_\text{max}\omega^2$</​color>​ +  - What is the index of refraction ​of the material ​for red light? ​(pts)  
-    * <color green>​the greatest values are for the high-frequency sound</​color>​ +    * <color green>​...</​color>​ 
-  - Find the maximum velocity and the maximum acceleration ​of the eardrum ​for vibrations of amplitude $1.0\times 10^{-8}\,$m at a frequency of 20.0 kHz. (pts)  +      * <color green>...</​color>​ 
-    * <color green>$v_\text{max}$ $=x_\text{max}\omega$ $=x_\text{max}(2\pi f)$ $=1.0\times 10^{-8}\,​$m$\,​\cdot\,​6.283\cdot 20\times 10^3\,$Hz $=1.26\times 10^{-3}\frac{\text m}{\text s}$ </​color>​ +  - What is the speed of red light in the material? (pts) 
-    * <color green>$a_\text{max}$ $=x_\text{max}\omega^2$ $=x_\text{max}(2\pi f)^2$ $=1.0\times 10^{-8}\,​$m$\,​\cdot\,​(6.283\cdot 20\times 10^3\,​$Hz$)^2=158\,​\frac{\text m}{\,{\text s}^2}$ ​</​color>​ +    * <color green>...</​color>​ 
-  - What is the period of a complete oscillation ​of the ear drum at this frequency? (pts) +      * <color green>...</​color>​ 
-    * <color green>$T=\frac{1}{f}$ $=\frac{1}{20\times 10^3\,​{\text{Hz}}}$ $=5.0\times 10^{-5}\,$s</​color>​ +  - What is Brewster'​s angle for red light going from vacuum to the mystery material? (3 pts) 
-  - Using a crude model of the eardrum as a mass (3.0 mg) on a spring, what would be the spring constant of the eardrum, assuming the resonance frequency of 20.0 kHz? (3 pts) +    * <color green>...</​color>​ 
-    ​* <color green>$T=2\pi\sqrt{\frac{m}{k}}$</​color>​ +      * <color green>​...</​color>​ 
-    * <color green>$\left(\frac{T}{2\pi}\right)^2=\frac{m}{k}$</​color>​ +  - Would the critical angle for blue light be greater or smaller than that of red light? ​(1 pt). Why? (pts) (Hint: You can safely make the assumption that this mystery material behaves like glass for the frequency dependence of the index of refraction.)  
-    * <color green>$k=\frac{4\pi^2m}{T^2}$ $=\frac{4\,​\cdot\,​3.14159^2\,​\cdot\,​3.0\times 10^{-6}\,​{\text{kg}}}{\big(5.0\times 10^{-5}\,​{\text s}\big)^2}$ $=4.74\times 10^4\frac{\text N}{\text m}$</​color>​ +    * <color green>...</​color>​
-  - The ear canal (external auditory canal) can be modeled as a tube with one closed end. If the length ​of the ear canal is 25 mm long and the speed of sound in air is 340 m/s, what is the fundamental ​(1<​sup>​st</​sup>​ harmonicof the ear canal? (pts)  +
-    * <color green>$f_1=\frac{v}{4L}$ $=\frac{340\,​\frac{\text m}{\text s}}{4\,​\cdot\,​25\times 10^{-3}\,​{\text m}}$ $=3400\,$Hz</​color>​+
  
exam_2_review.txt · Last modified: 2014/05/14 14:48 by wikimanager