The tube in Fig. 15.1 is filled with helium. What is the fundamental frequency of the tube if the ë in the figure is 65.55 cm? The speed of sound in helium is 1007 m/s.
A)2640.4 Hz
B)1320.2 Hz
C)38.4 Hz
D)15.4 Hz

Question

Quizplus · Accepted Answer

The fundamental frequency of a tube can be calculated using the formula $f = \frac{v}{2L}$, where $v$ is the speed of sound in the medium (in this case, helium) and $L$ is the length of the tube. Given that the length of the tube ($\lambda$) is 65.55 cm (or 0.6555 meters) and the speed of sound in helium is 1007 m/s, the fundamental frequency is $f = \frac{1007}{2 \times 0.6555} = 768.5 Hz$. However, since none of the provided options match this calculation directly and considering the context of the question might imply considering the tube's length as half the wavelength for the fundamental frequency (which is a common approach for open tubes), the correct calculation should be reconsidered based on the given options and the nature of the question. Given the discrepancy in the initial explanation, let's correct the approach: For a tube filled with helium and considering the wavelength provided, if we were to calculate the fundamental frequency with a different interpretation of the tube's characteristics (e.g., an open or closed tube), we would use the relationship between the wavelength and the frequency differently. However, without further details on the tube's type (open or closed at both ends), the direct calculation provided doesn't match the options given. The correct approach for an open tube, where the length of the tube is equal to half the wavelength for the fundamental frequency, would be $f = \frac{v}{\lambda}$. Given the speed of sound in helium (1007 m/s) and a wavelength of 65.55 cm (or 0.6555 meters for the fundamental harmonic), the calculation should directly relate to these values. Given the misunderstanding in the initial explanation, it's important to note that the fundamental frequency calculation directly depends on the accurate interpretation of the tube's characteristics and the given data. The provided answer choices suggest specific frequencies that would result from particular calculations, but without a clear match to the standard formula or a direct explanation for each choice, there's a need to reevaluate the answer based on the correct understanding of the physical principles involved. Therefore, the correct answer should reflect a calculation based on the given speed of sound in helium and the specific conditions of the tube as described in the question, which might involve more specific considerations of the tube's characteristics and the sound wave's behavior in such a medium.

The Tube in Fig