Anemometer · Estonian PhO 2016 #9

Physics · mechanics

Problem

An ultrasonic anemometer measures wind speed by determining the time it takes for an audio signal to reach the sensors from an audio source. Let the audio source be at the origin O=(0;0)O=(0;0) and three sensors at points with the coordinates A=(0;a)A=(0;a), B=(a;0)B=(a;0) and C=(−a;0)C=(-a;0) where a=\SI211.1mma=\SI{211.1}{mm} (let us make a simplifying assumption that the dimensions of both the audio source and the sensors are negligible). The anemometer is held so that all the sensors are located on the same horizontal plane and the times taken for the audio signal to reach the sensors are measured to be accordingly tA=\SI627,0\microst_A=\SI{627,0}{\micro s}, tB=\SI625,2\microst_B=\SI{625,2}{\micro s} and tC=\SI603,4\microst_C=\SI{603,4}{\micro s}. What is the speed of wind? You can use reasonable simplifying approximations for the calculations.

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