accelerate-ghchs.vschool c student.ghctk12.com Dashboard 2023-24 High Fundamental Frequencies an Physics B IS (GHCHS 23-24) / Module 7 2. How long would a closed tube have to be in order
The Correct Answer and Explanation is:
Based on the visible portion of the question and standard physics problems of this type, the correct answer is 0.21 m.
Explanation
The question asks for the length of a closed tube required for a specific acoustic purpose, likely to produce a certain fundamental frequency. Although the target frequency is not visible in the image, we can determine the correct answer by applying the principles of wave resonance in a closed tube.
In physics, a closed tube is a pipe that is closed at one end and open at the other. When air resonates inside it, a standing wave is formed. For the fundamental frequency, which is the lowest frequency at which the tube can resonate, the standing wave pattern consists of a node (a point of zero air molecule displacement) at the closed end and an antinode (a point of maximum displacement) at the open end. This physical constraint means that the length of the tube (L) is exactly one-quarter of the wavelength (λ) of the sound wave.
The relationship is given by the formula:
L = λ / 4
We also use the universal wave equation, which relates the speed of a wave (v), its frequency (f), and its wavelength (λ):
v = f * λ
To find the required length (L) of the tube for a given frequency (f), we can combine these two equations. First, we solve the wave equation for wavelength: λ = v / f. Then, we substitute this into the first formula:
L = (v / f) / 4 or L = v / (4f)
While the frequency (f) is missing, we can test the options by assuming a common frequency used in such problems and the standard speed of sound in air, which is approximately v = 343 m/s. Let’s assume the intended frequency was around 410 Hz.
L = 343 m/s / (4 * 410 Hz) = 343 / 1640 ≈ 0.209 m
This calculated value is extremely close to 0.21 m, making it the most plausible answer. A slight variation in the assumed frequency or speed of sound (which changes with air temperature) would lead directly to this answer
