Question

Write down the formula relating frequencies f_n for higher natural modes of vibration to the fundamental mode frequency f₁

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

F₁ = V/2L

F₂ = 2*V/2L =2*F₁

F₃ = 3*F₁

so  

F_n = n*F₁

CASE 2

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

F_n = (2n-1) *V/4L

F₁ = V/4L

F₂ = 3*V/4L = 3*F₁

F₃ = 5*V/4L = 5*F₁

F_n = (2n-1) *F₁

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