Question

Write down the formula relating frequencies f_{n} for
higher natural modes of vibration to the fundamental mode frequency
f_{1}

Answer #1

there are two case

rest all other fall in two category

CASE 1

both side open organ pipe , string fixed at both end , or string not fixed at both end

in this case

here v= speed of sound in pipe , speed of wave in rope

L = length of pipe or length of string

F_{n} =n *V/2L

F_{1} = V/2L

F_{2} = 2*V/2L =2*F_{1}

F_{3} = 3*F_{1}

so

**F _{n} = n*F_{1}**

CASE 2

one side open organ pipe , string fixed at one end , water column with tuning fork

F_{n} = (2n-1) *V/4L

F_{1} = V/4L

F_{2} = 3*V/4L = 3*F_{1}

F_{3} = 5*V/4L = 5*F_{1}

**F _{n} = (2n-1) *F_{1}**

****************************************************************************

Goodluck for exam Comment in case any doubt, will reply for
sure..

6. (a) Calculate the first three frequencies of axial vibration
of a bar fixed at one end.
(b) Derive the
orthogonality condition of natural modes
of vibration in axial
direction.
(c)
Discuss the modal analysis
method.
(d). Determine the
first two frequency by Rayleigh-ritz method,
assuming

For a 2DOF system, how many natural frequency (frequencies) does
it have? How many vibration(s) could it possibly have?

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