Longest Wavelengths in 128 cm Tube: Open at Both/One End

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In summary, a 128 cm tube is commonly used for studying longest wavelengths in acoustics and other physical phenomena due to its ability to produce clear and accurate results. The fact that the tube is open at both ends allows for the measurement of the longest wavelength, which is the distance between two adjacent nodes in a standing wave pattern. This measurement can also be obtained with a tube that is open at only one end, but the results may differ slightly. Factors such as temperature, humidity, tube material, and obstructions can affect the accuracy of these measurements. The data obtained from measuring longest wavelengths in a 128 cm tube can be used in various scientific research, such as studying sound waves, light waves, and material properties.
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spokorne
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Homework Statement



What are the three longest wavelengths for standing sound waves in a 128-cm-long tube that is (a) open at both ends and (b) open at one end, closed at the other?

Homework Equations


W=V/F


The Attempt at a Solution



128 cm because nothing bigger could fit in the tube
 
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  • #2
In the fundamental mode of vibration, the wavelength in open pipe is λ/2 and in closed pipe λ/4.
 
  • #3
.

I would like to clarify that the longest wavelengths for standing sound waves in a 128-cm-long tube will depend on the speed of sound in the medium inside the tube. The equation W=V/F is correct, but it is important to note that the speed of sound can vary depending on the temperature, pressure, and composition of the medium. Therefore, the exact values of the longest wavelengths cannot be determined without knowing the specific conditions of the experiment.

That being said, assuming the speed of sound in the medium is constant, the three longest wavelengths for standing sound waves in a 128-cm-long tube that is open at both ends will be 128 cm, 64 cm, and 42.7 cm (assuming the speed of sound is equal to 342 m/s, the speed of sound in air at room temperature).

For a tube that is open at one end and closed at the other, the three longest wavelengths will be 256 cm, 128 cm, and 85.3 cm (again, assuming the speed of sound is equal to 342 m/s).

It is also worth mentioning that in both cases, there are an infinite number of possible wavelengths for standing sound waves, with each successive wavelength being an integer multiple of the longest wavelength.
 

1. What is the significance of a 128 cm tube in relation to longest wavelengths?

A 128 cm tube is a commonly used length for studying longest wavelengths in acoustics and other physical phenomena. This length has been found to produce the clearest and most accurate results for measuring the longest wavelengths.

2. How does the fact that the tube is open at both ends affect the wavelength measurement?

The fact that the tube is open at both ends allows for the wave to travel freely in both directions, resulting in a standing wave pattern. This allows for the measurement of the longest wavelength, which is the distance between two adjacent nodes in the standing wave pattern.

3. Can the tube be open at only one end and still measure longest wavelengths?

Yes, the tube can be open at only one end and still produce a standing wave pattern. However, the measurement of the longest wavelength will be slightly different as it will be the distance between the open end and the first node of the standing wave.

4. What factors can affect the accuracy of measuring longest wavelengths in a 128 cm tube?

The accuracy of measuring longest wavelengths can be affected by the temperature and humidity of the environment, as well as the quality and composition of the tube material. The presence of any obstructions or irregularities in the tube can also affect the results.

5. How can the data obtained from measuring longest wavelengths in a 128 cm tube be used in scientific research?

The data obtained from measuring longest wavelengths can be used to study various physical phenomena, such as sound waves, light waves, and even ocean waves. This data can also be used to understand the properties of different materials and their interactions with waves.

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