# Open and Closed Tube Resonance

## Formulas Used

1. A homeowner removes an old satellite dish from his backyard, leaving a circular pipe 3.2 inches in diameter sticking out of the ground. If the top end of the pipe is 41 inches above the ground, what is the resonant wavelength as the wind blows across the pipe?
2. A musician is trying to create a homemade wind instrument from a pipe with an inner diameter of 1.5 cm. If she wants the fundamental wavelength to be 0.649 m when the pipe is open at both ends, what length of pipe should she cut?
3. A child blows over the top of a bottle that is 16 cm high and 3.0 cm in diameter at the mouth. If the speed of sound is 339 m/s, what frequency will the child hear?
4. One end of an open tube is placed near a large speaker. The tube is 2.7 m long and has an inner diameter of 7.9 cm. If the speed of sound is 3.40 × 102 m/s, what frequency of sound should be played in order to hear a loud resonant tone?
5. A craftsman is making a wind instrument to be played at an outdoor ceremony. He has an open pipe with an inner diameter of 1.4 cm, and he wants a particular pipe to have a frequency of 490 Hz. If the temperature is expected to be 100 °C, how long does the pipe need to be?

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