A closed pipe of length 10 cm has its fundamental frequency half that of the second overtone of an open pipe. The length of the open pipe

Question

A closed pipe of length 10 cm has its fundamental frequency half that of the second overtone of an open pipe. The length of the open pipe (A) 10 cm (B) 20 cm (C) 30 cm (D) 40 cm

Tardigrade Admin · Accepted Answer

l=0.1 m Fundamental frequency of pipe (f1)=(v/4 l) or f1=(v/0.4) Frequency of 2 text nd overtone of open pipe 2: f2=(3 v/2 l) 2 f1=f2 2 × (v/0.4)=(3 v/2 l) l=0.3 m

Q. A closed pipe of length $10 c m$ has its fundamental frequency half that of the second overtone of an open pipe. The length of the open pipe

10 cm

20 cm

30 cm

40 cm

$l = 0.1 m$
Fundamental frequency of pipe $(f_{1}) = \frac{v}{4 l}$ or $f_{1} = \frac{v}{0.4}$
Frequency of $2^{nd}$ overtone of open pipe $2$ :
$f_{2} = \frac{3 v}{2 l}$
$2 f_{1} = f_{2}$
$2 \times \frac{v}{0.4} = \frac{3 v}{2 l}$
$l = 0.3 m$

Q. A closed pipe of length 10cm has its fundamental frequency half that of the second overtone of an open pipe. The length of the open pipe