Question

show that the fundamental frequency of an open pipe is twice the fundamental frequency of the closed pipe of the same length?​

Answer 1

fundamental frequency of open pipe = 2 × fundamental frequency of closed pipe.

we have to show that fundamental frequency of an open pipe is twice the fundamental frequency of the closed pipe of the same length.

let length of pipe is l and wavelength of resonating wave is λ.

from figure - 1, λ/4 + λ/4 = l

⇒2λ/4 = λ/2 = l

⇒λ = 2l

now, fundamental frequency of open pipe , f = v/λ = v/2l .......(1)

again for closed pipe.

from figure -2, λ/4 = l

⇒λ = 4l

fundamental frequency of closed pipe, f = v/λ = v/4l.......(2)

from equations (1) and (2) it is clear that,

fundamental frequency of open pipe = 2 × fundamental frequency of closed pipe.

Answer 2

$\huge\bold\purple{Answer:-}$

fundamental frequency of open pipe = 2 × fundamental frequency of closed pipe. we have to show that fundamental frequency of an open pipe is twice the fundamental frequency of the closed pipe of the same length. let length of pipe is l and wavelength of resonating wave is λ. again for closed pipe.