A closed organ pipe and an open organ pipe have their first overtones identical in frequency…

Q: A closed organ pipe and an open organ pipe have their first overtones identical in frequency. Their lengths are in the ratio

(a) 1 : 2

(b) 2 : 3

(c) 3 : 4

(d) 4 : 5

Ans: (c)

Sol: In a closed organ pipe

$ \displaystyle \nu_3 = 3 (\frac{v}{4l_1})$

In a open organ pipe

$ \displaystyle \nu_2 = 2 (\frac{v}{2 l_2})$

$ \displaystyle \nu_3 = \nu_2 $

$\displaystyle 3 (\frac{v}{4l_1}) = 2 (\frac{v}{2 l_2}) $

$ \displaystyle \frac{l_1}{l_2} = \frac{3}{4}$