Mission SM9 Mathematics for Open-End Air Columns
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Consider the standing wave pattern for an open-end air column. The speed of sound in the air is 335 m/s and the frequency associated with this pattern is 278 Hertz. Determine the wavelength (in centimeters) associated with this pattern and the length (in centimeters) of the air column.
(Note: Your numbers may be different from the numbers listed.)
Each harmonic frequency is associated with a standing wave pattern. The standing wave pattern shows a unique relationship between the wavelength of the waves that create the pattern and a length measured along the medium between two points on the pattern. Every nodal position on the pattern is separated from the next adjacent nodal position by one-half of a wavelength. Similarly, every antinodal position on the pattern is separated from the next adjacent antinodal position by one-half of a wavelength.
The speed of the sound waves are stated in units of meters per second. The length and wavelength must be determined in units of centimeters. At some time during the solution of this problem, you will have to convert the unit meters to centimeters. Always be units-conscious.
- Calculate the wavelength of the wave using the wave equation provided in the Formula Frenzy section.
- Convert the units on wavelength to centimeters. Enter the answer for wavelength.
- Analyze the provided standing wave pattern to determine the relationship between the wavelength of waves and the length of the air column. See the Know the Law section.
- Use the length-wavelength relationship to calculate the length of the air column in units of centimeters. Enter the answer for length.
