p235w11_practice_exam_3_2_sol

p235w11_practice_exam_3_2_sol - Physics 235 Winter 2011...

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Physics 235 Winter 2011: Practice Exam #3 Version 2 Solutions Form #1 Please print your name:_____________________________________________________ Instructions 1. Fill in your name above 2. This will be a 1 hour 50 minute, closed book exam. 3. You may use a calculator, please do not share calculators 4. For this exam, you can bring three 3x5 cards with any notes you wish to have. You will also be given all physical constants that you might require to do all the problems.
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1: (10 points) A bat engaged in echolocation emits 30 ms long sound pulses with a frequency of 75,000 Hz and with an initial intensity of 10 -2 W/m 2 . The speed of sound in air is 340 m/s. a: (2 points) This sound strikes a moth 22 m away from the bat. What is the intensity of the sound, measured in decibels, when it strikes the moth? There is no way to do this without knowing where the initial intensity is measured. Let’s assume this is very close to the bat, we’ll take 10 cm away. Now we can work out the intensity at the moth. 2 00 0 2 0 22 0 22 0 2 22 22 22 22 22 10 10 10 10 12 2 12 2 22 P = 4 4 4 44 0.1 10log 10log 20log 100 20log 53.2 dB 10 W/m 10 W/m 22 P Ir I r rI r P II rr r I dB r        b: (3 points) The sound bounces off the moth and returns to the bat. What is the intensity in decibels of the reflected sound the bat hears?    2 moth 0 moth 0 moth 0 return 0 4 22 22 22 m o t h 22 10 10 10 -12 2 2 2 22 P4 π r4 π π I= = = I r 4 π π r r 0.01×0.1 dB =10log +20log =100+20log = 13.7 dB 10 W/m r 22 c: (2 points) How much time elapses between the beginning of the bat’s sound pulse and the return of the echo? 2 2 m 65 ms 340 m/s s d t v  d: (3 points) If the bat is flying toward the moth at a speed of 4 m/s, and the moth is hovering at rest, what is the frequency of the reflected sound the bat hears? 0 340 340 4 1.023 76,785 Hz 340 4 340 ss b sb s vv v ff f f vv v
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2: (5 points) Two speakers emit sound waves in synch with one another. They are separated by a distance of 2.0 m. The frequency of the sound they produce is 206 Hz. Consider a point a distance x from speaker A, along the line between them. a: (3 points) For what values of x between the speakers will there be constructive interference between the two? = 340 m/s / 206 Hz = 1.65 m. The path length difference PL = (2-x) – x = 2-2x We want this to be an integer multiple of , so 2-2x = n , which gives x = 1 - n /2 which has values x = 0.175, 1, 1.825 (for n = 1, 0, and -1)…. b: (2 points) For what values of x will there be destructive interference? PL = 2-2x = (2n+1) /2 x = 1 – (2n+1) /4 x = 0.5875, 1.4125 (for n = 0 and n = -1) 3: (5 points) Explain why you can see “images” when you look in a mirror but not when you look in a wall. To form images, a surface must reflect light, but it must also be smooth on the scale of the wavelength of light; 500 nm or so. Most surfaces are quite rough on this scale, and reflect light diffusely (in every direction) instead of specularly (only with an angle of reflection equal to the angle of incidence). When reflections are diffuse, they do not form images, because there is no way to tell where reflected light originally came from.
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p235w11_practice_exam_3_2_sol - Physics 235 Winter 2011...

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