Question

Two closed organ pipes A and B, have the same length and A is wider than B. They resonate in the fundamental mode at frequencies $n_A$ and $n_B$ respectively

• A. $n_A=n_B$
• B. $n_A>n_B$
• C. $n_A<n_B$
• D. $\text{Either (2) or (3) depending on the ratio of their diameters}$

Answer 1

The correct option is C $n_A<n_B$

Let $l=$ length of the pipe

$d=$ diameter of the pipe

For fundamental mode of vibration , $=\frac{\lambda }{4}=l+0.3d$

So, frequency $\left(\nu \right)=\frac{v}{\lambda }=\frac{v}{4(l+0.3d)}$

So, as A is wider it has greater d

So, ${\nu }_A$ < ${\nu }_B$.