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?