A vertical tube closed at its lower end contains an air column of length 0.75m. The column resonates in its fundamental mode at room temperature where the speed of sound is 340ms−1.
(a) Calculate the frequency produced by the air column.
(b) Water is slowly poured into the tube, reducing the length of the air column to 0.45m. Determine the new fundamental frequency.
(c) The tube is now opened at the top end, converting it into an open pipe of length 0.45m. Find the frequency of the second overtone produced by this open pipe.
(d) Compare the frequencies obtained in parts (b) and (c). State which one is higher and compute their ratio.
a. (a) Fundamental frequency for 0.75 m closed pipe.
b. (b) Fundamental frequency after water reduces length.
c. (c) Second overtone frequency for 0.45 m open pipe.
d. (d) Comparison and ratio of frequencies.