Question

An open pipe and a closed pipe are in resonance with each other with their first overtones. The ratio of their lengths are

• A. 4:3
• B. 3:4
• C. 1:3
• D. 3:1

Answer 1

Answer: (A)

4:3

First overtone in open pipe is $2{\nu }_o=\frac{2v}{2L_1}$

First overtone in closed pipe is $3{\nu }_c=\frac{3v}{4L_2}$

Now by problem:

$2{\nu }_o=3{\nu }_c$

$\frac{2\nu }{2L_1}=\frac{3\nu }{4L_2}$

$\frac{L_1}{L_2}=\frac{4}{3}$