Consider a beam of length , whose weight is negligible in the elasticity equations, supported freely at both ends (so the slope of the beam is unconstrained at the ends) Show that the frequencies of standing flexural waves satisfy where A is the cross sectional area, and n is an integer Now repeat the exercise when the ends are clamped Based on your result, explain why xylophones dont have clamped ends (0) l 2 D (2) PA 1 2

Question: Consider a beam of length , whose weight is negligible in the elasticity equations, supported freely at both ends (so the slope of the beam

Consider a beam of length ℓ, whose weight is negligible in the elasticity equations, supported freely at both ends (so the slope of the beam is unconstrained at the ends). Show that the frequencies of standing flexural waves satisfy

(0) = l 2 D (2)" PA 1/2

where A is the cross sectional area, and n is an integer. Now repeat the exercise when the ends are clamped. Based on your result, explain why xylophones don’t have clamped ends.

(0) = l 2 D (2)" PA 1/2

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For a beam of length with negligible weight the equation of motion for flexural waves is given by d2dx2 EI d2wdx2 A 2 w 0 where wx is the transverse d... View full answer

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