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Unformatted text preview: practice 14 GADHIA, TEJAS Due: Apr 25 2007, 4:00 pm 1 Question 1 part 1 of 2 10 points In order to be able to determine her speed, a skydiver carries a tone generator. A friend on the ground at the landing site has equip- ment for receiving and analyzing sound waves. While the skydiver is falling at terminal speed, her tone generator emits a steady tone of 1690 Hz. Assume the air is calm and that the sound speed is 343 m / s, independent of altitude. If her friend on the ground (directly be- neath the skydiver) receives waves of fre- quency 2920 Hz, what is the skydivers speed of descent? Correct answer: 144 . 483 m / s (tolerance 1 %). Explanation: Let : v = 343 m / s , f e = 1690 Hz , and f g = 2920 Hz . Since the diver (the source of the sound waves) is moving toward her friend on the ground (the receiver of the waves), the Doppler formula takes the form f g = f e v v- v diver , so 1- v diver v = f e f g . Solving for v diver , we have v diver = v parenleftbigg 1- f e f g parenrightbigg = (343 m / s) parenleftbigg 1- 1690 Hz 2920 Hz parenrightbigg = 144 . 483 m / s . Question 2 part 2 of 2 10 points If the skydiver were also carrying sound- receiving equipment sensitive enough to de- tect waves reflected from the ground, what frequency would she receive? Correct answer: 4150 Hz (tolerance 1 %). Explanation: If the waves are reflected, and the skydiver is moving towards them, we have f rec = f g parenleftbigg v + v diver v parenrightbigg = (2920 Hz) parenleftbigg 343 m / s + 144 . 483 m / s 343 m / s parenrightbigg = 4150 Hz . Question 3 part 1 of 1 10 points A supersonic aircraft is flying parallel to the ground. When the aircraft is directly overhead, an observer sees a rocket fired from the aircraft. 10 . 2 s later the observer hears the sonic boom, followed 3 . 61 s later by the sound of the rocket engine. What is the Mach number of the aircraft? Correct answer: 1 . 48335 (tolerance 1 %). Explanation: Let : t 1 = 10 . 2 s and t 2 = 3 . 61 s . Let be the half angle of the shock front. Then sin = v v s = 1 N M , where N M is the Mach number. Let h be the height of the plane and x be the distance traveled by the plane when the observer hears the sonic boom. Then from the geometry tan = h x = v ( t 1 + t 2 ) v s t 1 = t 1 + t 2 N M t 1 . Therefore using the trigonometric identity cos = sin tan = N M t 1 t 1 + t 2 1 N M , practice 14 GADHIA, TEJAS Due: Apr 25 2007, 4:00 pm 2 = arccos parenleftbigg t 1 t 1 + t 2 parenrightbigg = arccos parenleftbigg 10 . 2 s 10 . 2 s + 3 . 61 s parenrightbigg = 42 . 3881 , and the Mach number is N M = 1 sin = 1 sin42 . 3881 = 1 . 48335 . Question 4 part 1 of 2 10 points A block of volume 0 . 59 m 3 floats with a fraction 0 . 74 of its volume submerged in a liquid of density 1340 kg / m 3 , as shown in the figure below....
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