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{"ops":[{"insert":"Suppose that we have a sonar that can emit a sound pulse (\u201cping\u201d) with a frequency of\n440 Hz when the source is stationary. The sonar can also detect pings as they are\nreflected by its surroundings (\u201cechoes\u201d). Assume the speed of sound to be 343 m\/s. The\nobstacle is unknown to the sonar, but for the sake of simplicity, assume that it has a\nlarge flat surface.\n\nFirst consider the case where the sonar is stationary while the obstacle is moving with\nconstant velocity.\n1. If the echo received by the sonar has a frequency of 392 Hz, how fast and in what\ndirection is the obstacle moving? (5 pts)\n2. The first echo was detected 0.400 s after the first ping was sent. Calculate the\ndistance between the sonar and the obstacle at the moment when:\na. the first ping was reflected (5 pts)\nb. the first ping was sent (5 pts)\nc. the first echo was detected (5 pts)\n\nNext consider the case where the obstacle is stationary while the sonar is moving with\nconstant velocity.\n3. The ping reflected by the obstacle has a frequency of 740 Hz.\na. How fast and in what direction is the sonar moving? (5 pts)\nb. What would be the frequency of the echo as it is detected by the sonar?\n(Treat the obstacle as the source and the sonar as the observer.) (5 pts)\n4. The obstacle reflected the ping 0.250 s after it was sent by the sonar.\na. How far was the sonar from the obstacle when the ping was sent? (5 pts)\nb. How far was the sonar from the obstacle when the echo is reflected? (5 pts)\nc. How much time would the echo spend travelling before it is received by the\nsonar? (5 pts)\n\nLastly, consider the case where both the sonar and the obstacle are moving. We set the\nsonar to be moving with velocity 1.00 m\/s toward the obstacle. The velocity of the\nobstacle is unknown.\n5. The ping reflected by the obstacle has a frequency of 220 Hz.\na. How fast and in what direction is the obstacle moving? (5 pts)\nb. What would be the frequency of the echo as it is detected by the sonar? (5\npts)\n\n6. The obstacle reflected the ping 0.300 s after it was sent by the sonar.\na. What was the distance covered by the ping as it travelled from the sonar to\nthe obstacle? (5 pts)\nb. What is the distance between the sonar and the obstacle as the ping is\nreflected? (5 pts)\nc. How far are the sonar and obstacle from each other at the moment the echo\nis received by the sonar? (5 pts)\n"}]}

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