Chapter 16, Problem 3P

You are working for a plumber who is laying very long sections 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 compressional 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 smartphone, you will measure the time interval Δt 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 measure the length, you must derive an equation that relates the length L of the pipe numerically to the time interval Δt. (b) You measure a time interval of Δt = 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 calculate by how many centimeters your calculation of the length might be in error.