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Unformatted text preview: s the wave equation (331), represents the speed of sound in air. The boundary conditions are that zero longitudinal displacement of the air at the closed end of the pipe- - and - - that is, there is
- - that is, there is zero pressure perturbation at the open end of the pipe (because the small pressure perturbation in the pipe is not
intense enough to modify the pressure of the atmosphere external to the pipe). Let us write the displacement
pattern associated with the standing wave in the form
(333) where , , condition , and are constants. This expression automatically satisfies the boundary . The other boundary condition is satisfied provided (334) which yields
(335) where the mode number is a positive integer. Equations (331) and (333) give the dispersion relation (336) Hence, the th normal mode has a wavelength (337) and an oscillation frequency (in hertz)
(338) where is the frequency of the fundamental harmonic (i.e., the normal mode with the lowest oscillation frequency). Figure 34 i...
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