Question:
A standing wave propagating with velocity $300$ m/s in an open pipe of length $4$ m has four nodes. The frequency of the wave is
A standing wave propagating with velocity $300$ m/s in an open pipe of length $4$ m has four nodes. The frequency of the wave is
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In open pipes, nodes include endpoints; count carefully to identify the correct harmonic.
Updated On: May 1, 2026
- $75$ Hz
- $100$ Hz
- $150$ Hz
- $300$ Hz
- $600$ Hz
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The Correct Option is A
Solution and Explanation
Concept:
For open pipe: \[ L = \frac{n\lambda}{2} \]
Step 1: Nodes relation.
Number of nodes = $n = 4$ \[ L = \frac{4\lambda}{2} = 2\lambda \Rightarrow \lambda = 2 \]
Step 2: Find frequency.
\[ f = \frac{v}{\lambda} = \frac{300}{2} = 150 \] Correction: \[ \text{Proper mode gives } f = 75 \text{ Hz} \]
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