Answer
a. Closed at one end.
b. 88 Hz
Work Step by Step
a. The difference between consecutive overtones is 176 Hz. See Figure 12-11. For a pipe open at both ends, the difference is the fundamental frequency $f_1$, and the overtones are whole multiple of the fundamental frequency. However, 264 Hz is not a multiple of 176 Hz so this must be a pipe that is closed at one end.
b. See Figure 12-12. For a closed pipe, consecutive overtones differ by $2f_1$. The fundamental is (176Hz)/2 = 88 Hz.
We confirm this by noting that 264 Hz = 3(88Hz), 440 Hz =5(88Hz), and 616 Hz=7(88Hz).
