Length of Closed Organ Pipe – Rankers Physics
Topic: Waves
Subtopic: Standing Wave in String and Organ Pipe

Length of Closed Organ Pipe

Velocity of sound in air is \(320\text{ m/s}\). If frequency of \(1^{\text{st}}\) overtone of a closed organ pipe is \(480\text{ Hz}\), then the length of the organ pipe is
\(100\text{ cm}\)
\(25\text{ cm}\)
\(75\text{ cm}\)
\(50\text{ cm}\)

Solution:

The frequency of the \(1^{\text{st}}\) overtone (third harmonic) of a closed organ pipe is given by \(f = \frac{3v}{4L}\). Given \(f = 480\text{ Hz}\) and \(v = 320\text{ m/s}\), we have \(480 = \frac{3 \times 320}{4L} ⇒ L = \frac{960}{1920} = 0.5\text{ m} = 50\text{ cm}\).

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