Question

Two open organs pipes of fundamental frequencies ${\upsilon }_1$ and ${\upsilon }_2$ are joined in series. The fundamental frequency of the new pipe so obtained will be:

• A. ${\upsilon }_1+{\upsilon }_2$
• B. $\frac{{\upsilon }_1{\upsilon }_2}{({\upsilon }_1+{\upsilon }_2)}$
• C. $\frac{{\upsilon }_1{\upsilon }_2}{{\upsilon }_1-{\upsilon }_2}$
• D. $\sqrt{{\upsilon }_1^2+{\upsilon }_2^2}$

Answer 1

Answer: (B)

$\frac{{\upsilon }_1{\upsilon }_2}{({\upsilon }_1+{\upsilon }_2)}$

${\upsilon }_1=\frac{\nu }{2L_1}$ .....(i)
${\upsilon }_1=\frac{\nu }{2L_2}$ .....(ii)
When these two pipes are joined in series, the fundamental frequency of the new pipe is
$\upsilon =\frac{\nu }{2(L_1+L_2)}=\frac{\nu }{2L_1+2L_2}$
$\frac{\nu }{\frac{\nu }{{\upsilon }_1}+\frac{\nu }{{\upsilon }_2}}$ (Using (i) and (ii))
$\frac{{\upsilon }_1{\upsilon }_2}{{\upsilon }_2+{\upsilon }_1}$