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Question bank: Waves: Vibration in Sound Tubes

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Question 1:

Medium

A sound tube, used in a laboratory experiment, has one open end and one closed end. During the experiment, the tube is excited by a sound wave to produce vibrations in a standing wave pattern. What is the length of the tube, given that the first harmonic occurs at a frequency of 170 Hz and the speed of sound in air is 340 m/s?
Waves: Vibration in Sound Tubes
Question 2:

Medium

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Waves: Vibration in Sound Tubes
Question 3:

Hard

A physics student is studying the acoustic properties of sound tubes and decides to conduct a practical experiment to verify the resonance frequencies in an open tube and a closed tube. He starts with the open tube, which has a length L and a fundamental frequency f1. Next, he observes the second harmonic of the tube, which occurs when the column of air vibrates in two equal halves, presenting a frequency f2. For the closed tube, which has the same length L, he finds the fundamental frequency f3 and the third harmonic f4. Considering the speed of sound in the air as v=340 m/s, calculate the frequencies f1, f2, f3, and f4 for the open and closed tubes, respectively, and explain the relationship between the length of the tube and the values of the observed frequencies. Additionally, discuss how varying the length of the tube would alter the distance between the frequencies f1 and f2 in the open tube and between f3 and f4 in the closed tube, considering that the tube ends remain fixed during the experiment.
Waves: Vibration in Sound Tubes
Question 4:

Medium

You have been invited to design an adjustable sound tube for a concert hall. The orchestra wants the tube to be able to produce sound at two different fundamental frequencies: one for open tubes and another for closed tubes. To carry out this project, you should: a) Describe how vibration and the formation of standing waves work in open and closed sound tubes. b) Calculate the length of the tube needed to achieve a fundamental frequency of 440 Hz with a sound velocity of 340 m/s in the case of an open tube. c) Calculate the fundamental frequency of a closed tube of the same length as found in item b) and with the same sound velocity.
Waves: Vibration in Sound Tubes
Question 5:

Medium

An open-ended sound tube with a length of 85 cm is used to produce standing sound waves in the air. Considering the speed of sound in the air as 340 m/s, determine the frequency of the first harmonic (fundamental mode) and then, what would be the frequency of the third harmonic?
Waves: Vibration in Sound Tubes
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