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, then

• A. \(n_{A}=n_{B}\)
• B. \(n_{A}>n_{B}\)
• C. \(n_{A}\lt n_{B}\)
• D. either (2) or (3) depending on the ratio of their diameters

Hint:

A wider pipe has a larger end correction, so its effective length is longer and its frequency lower.

Answer 1

The Correct Option is C

Step 1: Write the Frequency Relation
$n\propto\dfrac{1}{L+0.3d}$ for equal speed of sound.

Step 2: Check the Diameters
A has a larger diameter, so the denominator is larger for A.

Step 3: Compare the options
The larger denominator gives a smaller frequency, so $n_{A}\lt n_{B}$. The option depending on diameter ratio is not needed because the result is always the same.

Final Answer:
The wider pipe resonates at a lower frequency. \[ \boxed{\text{(C) }n_{A}\lt n_{B}} \]