8. Waves in a Tube Standing waves in a violin string must have nodes at the ends of the string because the string is fixed at its endpoints. But this need not be the case with sound waves in a tube (such as a flute or an organ pipe). The figure shows some possible standing waves in a tube. Suppose that a standing wave in a tube 37.7 ft long is modeled by the function (x, 1) = 0.3 cos įx cos 50mt Here y(x, t) represents the variation from normal air pressure at the point x feet from the end of the tube, at time i seconds. (a) At what points x are the nodes located? Are the endpoints of the tube nodes? (b) At what frequency does the air vibrate at points that are not nodes?
8. Waves in a Tube Standing waves in a violin string must have nodes at the ends of the string because the string is fixed at its endpoints. But this need not be the case with sound waves in a tube (such as a flute or an organ pipe). The figure shows some possible standing waves in a tube. Suppose that a standing wave in a tube 37.7 ft long is modeled by the function (x, 1) = 0.3 cos įx cos 50mt Here y(x, t) represents the variation from normal air pressure at the point x feet from the end of the tube, at time i seconds. (a) At what points x are the nodes located? Are the endpoints of the tube nodes? (b) At what frequency does the air vibrate at points that are not nodes?
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Transcribed Image Text:8. Waves in a Tube Standing waves in a violin string must have nodes at the ends of the
string because the string is fixed at its endpoints. But this need not be the case with sound
waves in a tube (such as a flute or an organ pipe). The figure shows some possible standing
waves in a tube.
Suppose that a standing wave in a tube 37.7 ft long is modeled by the function
(x, 1) = 0.3 cos įx cos 50mt
Here y(x, t) represents the variation from normal air pressure at the point x feet from the
end of the tube, at time i seconds.
(a) At what points x are the nodes located? Are the endpoints of the tube nodes?
(b) At what frequency does the air vibrate at points that are not nodes?
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