You are working for a plumber who is laying very long sec- CR tions of copper...

You are working for a plumber who is laying very long sec- CR tions of copper pipe for a large building project. He spends a lot of time measuring the lengths of the sections with a measuring tape. You suggest a faster way to measure the length. You know that the speed of a one-dimensional com- pressional wave traveling along a copper pipe is 3.56 km/s. You suggest that a worker give a sharp hammer blow at one end of the pipe. Using an oscilloscope app on your smart- phone, you will measure the time interval Dt between the arrival of the two sound waves due to the blow: one through the 20.0 C air and the other through the pipe. (a) To mea- sure the length, you must derive an equation that relates the length L of the pipe numerically to the time interval Dt. (b) You measure a time interval of Dt =127 ms between the arrivals of the pulses and, from this value, determine the length of the pipe. (c) Your smartphone app claims an accuracy of 1.0% in measuring time intervals. So you calcu- late by how many centimeters your calculation of the length might be in error.

Answer will be a) L= (380 m/s)Dt b) 48.2 m c) 48 cm

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