Final answer:
The first harmonic of a closed pipe has a lower pitch than the first harmonic of an open pipe because the closed pipe supports a fundamental frequency corresponding to a quarter wavelength, resulting in a lower frequency and hence a lower pitch.
Step-by-step explanation:
The first harmonic of a pipe with one closed end will achieve a lower pitch than the first harmonic of a pipe with two closed ends. This is because a pipe that is closed at one end and open at the other (also known as a closed pipe) supports standing waves with a fundamental frequency that corresponds to a quarter wavelength fitting inside the pipe. In contrast, a pipe that is open at both ends (an open pipe) supports standing waves with a fundamental frequency that corresponds to half a wavelength fitting inside the pipe.
Because the wavelength for the fundamental frequency in a closed pipe is four times the length of the pipe (as opposed to twice the length for an open pipe), the fundamental frequency is lower, resulting in a lower pitch for the first harmonic. Additionally, the spectrum of overtones is different between the two types of pipes: a closed pipe only has odd harmonics, while an open pipe has both even and odd, giving it a richer set of overtones.