An open pipe resonates to a frequency 'f1' and closed pipe resonates to a frequency 'f2'. If they are joined together to form a longer tube. Then it will resonate to a frequency of (Neglect end correction

Question

An open pipe resonates to a frequency 'f1' and closed pipe resonates to a frequency 'f2'. If they are joined together to form a longer tube. Then it will resonate to a frequency of (Neglect end correction (A) (2 f1 f2/2 f2 + f1) (B) (f1 f2/f2 + 2 f1) (C) (2 f1 f2/f1 + f2) (D) (f1 f2/f1 + 2 f2)

Tardigrade Admin · Accepted Answer

f1=(V/2 ℓ 1) ℓ 1=(V/2 f1),ℓ 2=(V/4 f2) f=(V/4 ℓ ) f=(V/4 [(V)2 f1 + (V)4 f2] boxed/f = (f1 f2)f1 + 2 f2)

Q. An open pipe resonates to a frequency $^{'} f_{1}^{'}$ and closed pipe resonates to a frequency $^{'} f_{2}^{'} .$ If they are joined together to form a longer tube. Then it will resonate to a frequency of (Neglect end correction

$\frac{2 f _{1} f _{2}}{2 f _{2} + f _{1}}$

$\frac{f _{1} f _{2}}{f _{2} + 2 f _{1}}$

$\frac{2 f _{1} f _{2}}{f _{1} + f _{2}}$

$\frac{f _{1} f _{2}}{f _{1} + 2 f _{2}}$

$f_{1} = \frac{V}{2 ℓ _{1}}$ $ℓ_{1} = \frac{V}{2 f _{1}}, ℓ_{2} = \frac{V}{4 f _{2}}$
$f = \frac{V}{4 ℓ}$ $f = \frac{V}{4 [ \frac{V}{2 f _{1}} + \frac{V}{4 f _{2}} ]}$ $f = \frac{f _{1} f _{2}}{f _{1} + 2 f _{2}}$

Q. An open pipe resonates to a frequency ′f1′​ and closed pipe resonates to a frequency ′f2′​. If they are joined together to form a longer tube. Then it will resonate to a frequency of (Neglect end correction

2f2​+f1​2f1​f2​​

f2​+2f1​f1​f2​​

f1​+f2​2f1​f2​​

f1​+2f2​f1​f2​​