Question

The second overtone of an open pipe has the same frequency as the first overtone of a closed pipe 2 m long. The length of the open pipe is

• A. 8 m
• B. 4 m
• C. 2 m
• D. 1 m

Answer 1

The correct option is B 4 m

$l_0=$ length of organ pipe (open)

$l_c=$ length of close organ pipe

frequency of open pipe$=\frac{3V}{2l_0}$

frequency of close pipe $=\frac{3V}{2l_c}$

$\therefore \frac{3V}{2l_0}=\frac{3V}{4l_c}2l_0=4l_{c}2\times 2m=4m$

B is the correct option.