Final answer:
The claim is false; an open-pipe resonator supports resonant frequencies that are both even and odd multiples of the fundamental frequency, resulting in a richer sound with more overtones.
Step-by-step explanation:
The statement that 'An open-pipe resonator has resonant frequencies that are odd-numbered multiples of the fundamental' is false. Open-pipe resonators, which are open at both ends, support resonant frequencies that are both even and odd integer multiples of the fundamental frequency. This includes the fundamental frequency (first harmonic), as well as the second harmonic (first overtone), third harmonic (second overtone), and so on. In contrast, a closed-pipe resonator, which is closed at one end and open at the other, only supports odd-numbered harmonics.
When considering musical instruments, an open-pipe resonator produces a richer sound with more overtones, including even multiples of the fundamental frequency. Middle C, for example, will sound richer on an open-pipe instrument like a flute because it includes these even harmonics. On the other hand, a closed-pipe instrument, such as a clarinet, typically produces a sound with fewer overtones, comprising only odd-numbered multiples of the fundamental frequency.