A sound wave in a tube of length 30.0 cm open at both ends is very similar to a standing wave on a stretched string, except that there is an antinode of particle displacement at each opening. (Recall that a stretched string had a node at each end.) A tube open at both ends has the same pattern of normal modes (harmonics) as a stretched string. The end conditions are known as boundary conditions, and they determine the stable patterns that can oscillate in the tube forming standing waves. Make drawings of the first four harmonics in a tube open at both ends. Use sine waves (displacement on the y-axis) to represent the particle displacement (although the displacement is actually along the tube rather than perpendicular to it). Label the length of the tube, the nodes, and the antinodes in your drawings. Find the wavelengths of the first four harmonics.
A sound wave in a tube of length 30.0 cm open at both ends is very similar to a standing wave on a stretched string, except that there is an antinode of particle displacement at each opening. (Recall that a stretched string had a node at each end.) A tube open at both ends has the same pattern
of normal modes (harmonics) as a stretched string. The end conditions are known as boundary conditions, and they determine the stable patterns that can oscillate in the tube forming standing waves.
Make drawings of the first four harmonics in a tube open at both ends. Use sine waves (displacement on the y-axis) to represent the particle displacement (although the displacement is actually along the tube rather than perpendicular to it). Label the length of the tube, the nodes, and the antinodes in your drawings.
Find the wavelengths of the first four harmonics.
If the air in the tube is at temperature 20.00 ◦C or 293.15 K, what are the frequencies of the first four harmonics?
Find the frequencies of the first four harmonics if the temperature of the air in the tube increases to 30.00 ◦C or 303.15 K as a result of blowing hot air into it.
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