A student conducts an experiment to investigate stationary waves in a tube closed at one end by a movable piston. A small loudspeaker connected to a signal generator is positioned near the open end of the tube, as shown.
Due to the finite width of the tube, the displacement antinode at the open end occurs at a short distance eee (the end correction) outside the physical boundary of the tube.
The student finds that the first resonance occurs when the piston is at a distance x1 x_1\,x1 from the open end. As the piston is moved further back, the second resonance is heard when the piston is at a distance x2 x_2\,x2 from the open end.
Which expression gives the end correction e e\,e of the tube?
x2−3x12\frac{x_2 - 3x_1}{2}2x2−3x1
3x1−x22\frac{3x_1 - x_2}{2}23x1−x2
x2−2x1x_2 - 2x_1x2−2x1
x2−5x14\frac{x_2 - 5x_1}{4}4x2−5x1