HW4solution

HW4solution - AAE 334, Fall 2011, Homework 4 Due Wednesday,...

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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 ξ speaks at a volume (the amplitude of the pressure waves he or she emits as sound) () ξ γ . 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 2 r . What you hear at position x we will call H(x).
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