AAE 334, Fall 2011, Homework 4 Due Wednesday, August 31 at the beginning of class. Imagine that you are standing in line waiting to register early for a new third-semester aerodynamics course, AAE 335. There is a long line of your classmates in front of and behind you. Everyone but you is talking. Consider what you will hear – the sound from everyone added together. But you will hear louder and closer people better than quieter and distant people. Let’s describe this mathematically. You are at position x in line. You describe the other students by position ξ. The classmate at ξspeaks at a volume (the amplitude of the pressure waves he or she emits as sound) ()ξγ. The volume of your classmates’ voice drops with the square of the distance away from the speaker because of how the sound waves travel through the air. That is, a distance r away from the speaker at ξ, the amplitude of the sound is 2r. What you hear at position x we will call H(x).
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