To solve this problem, let's first understand how sound works in a closed pipe. A closed pipe has one end closed and another end open. Sound waves inside such a pipe create standing waves, where nodes (points of no movement) and antinodes (points of maximum movement) are formed.
For a closed pipe, the fundamental frequency (also called the first harmonic) has one node at the closed end and one antinode at the open end. The wavelength is four times the length of the pipe.
The overtone sequence for a closed pipe includes only odd harmonics: 1st (fundamental), 3rd, 5th, 7th, etc. The nth overtone is the 2nth + 1 harmonic. The equation for the frequency of a harmonic in a closed pipe is:
f_n = n * f_1, where f_n is the frequency of the nth harmonic and f_1 is the fundamental frequency
In this case, the fourth overtone corresponds to the 9th harmonic because 2 * 4 + 1 = 9. Therefore, we have:
900 Hz = 9 * f_1
To find the fundamental frequency (f_1), we solve for f_1:
f_1 = 900 Hz / 9
f_1 = 100 Hz
Therefore, the fundamental frequency is 100 Hz.