Final answer:
When a tube initially closed at one end with a fundamental frequency of 350 Hz is opened, its fundamental frequency becomes 700 Hz. This is due to the fact that an open tube supports a shorter wavelength, thus allowing for a higher fundamental frequency.
Step-by-step explanation:
Fundamental Frequencies of Open and Closed Tubes
When dealing with the acoustics of tubes, it's essential to understand how the configuration of the tube (open or closed) affects its fundamental frequency and overtones. A tube that is open at one end and closed at the other, such as the one mentioned with a fundamental frequency of 350 Hz, will have a lower fundamental frequency compared to one that is open at both ends.
Since the question states that a tube open at both ends has a fundamental frequency twice what it would have if closed at one end, opening the closed end of the tube would effectively double the observed fundamental frequency. Therefore, if the initially closed-end tube producing 350 Hz is opened, its new fundamental frequency would become 700 Hz.
In acoustics, this change occurs because the open tube supports a wavelength of 2L (where L is the length of the tube) for the fundamental mode, while a tube closed at one end supports a wavelength of 4L due to the need to form a node at the closed end and an antinode at the open end. By opening the previously closed end, the boundary conditions change, allowing the tube to support the shorter wavelength corresponding to the higher frequency.