Question

(a) Consider a rectangular drum lid with side lengths 4 and 5. If the natural frequencies lm,n are ordered from smallest to largest, write down the first three natural frequencies for wave speed c=1/T. Smallest Am,n Second smallest Am,n 13 Third smallest Im,ne (b) Degenerate modes are normal modes um,n and up, with identical natural frequencies, for which (m, n) + (8,9). For example, in the 2 x 1 rectangle, modes 04,1 and 42,2 are degenerate as they both have frequency 5. Given a drum with sides 4 and 8, find mode um,ne that is degenerate with v8,8- m = A n = (c) Consider a circular drum lid with radius 0.9 undergoing axisymmetric vibrations. Calculate any of the circular nodal lines s= A for mode 2, excluding A=0.9. You can use the zeros an (n=1,2,...) of Jo (1) given in the notes. Give your answer correct to two decimal places. If there are no nodal lines, write none. T=

Answer 1

AM given by = 4 units L2 = 5 units == formula used for Smallest frequenty of tractarguler Co drom did formal = 4, 1-10 → for fast Smallest faro quency: m=i, nal = 0.05095 2/4)*+63) f = 0.0509 HZ - for second smallest frequency m=2, na) fp = 7 27 (2)2+)2 = 0.0857 fo 0-0857 Hz → for thiend Smallest fierequency: m=3, n=1 fp = Žr l2)* +12 = 0.1235 fz = 0.1235 Hz Thank you