The Question is from NEET guide , and it was created by the author Mr. ANIL KUMAR.G

Question

Find the fundamental frequency of a closed pipe, if the length of the air column is $42\,\,m$. (speed of sound in air $ = 332\,m/\sec $

Mr. ANIL KUMAR.G · Accepted Answer

## CORE INFORMATION
✓ **Answer**: [A]
## CONCEPT FRAMEWORK
	**Primary Concept**: Fundamental frequency of a closed pipe
	**Related Topics**: Wave properties, Resonance, Sound waves
	**Prerequisites**: Understanding of wave speed, wavelength, and frequency relationship and the properties of a closed pipe.
## SOLUTION PATHWAY
**Given Information**:
	Length of the air column (L) = 42 m
	Speed of sound (v) = 332 m/s
	Pipe is closed at one end
**Method & Steps**:
	1. Determine the wavelength of the fundamental frequency in a closed pipe.
		Reasoning: In a closed pipe, the fundamental frequency corresponds to a quarter wavelength fitting within the pipe's length.
		Formula/Rule: $L = \frac{\lambda}{4}$
	2. Calculate the wavelength.
		Working:$\lambda = 4L = 4 	imes 42 = 168 \,m$
		Key Point: The wavelength is four times the length of the pipe.
	3. Calculate the frequency using the wave speed formula.
		Result: $f = \frac{v}{\lambda} = \frac{332}{168} \approx 1.976 \,Hz$
		Verification:  The calculated frequency is approximately 2 Hz
## OPTION ANALYSIS
[A] ✓: The fundamental frequency is approximately 2 Hz, as calculated.
[B] :x: 4 Hz is incorrect. This would correspond to a higher mode.
[C] :x: 7 Hz is incorrect. This does not correspond to the fundamental frequency.
[D] :x: 9 Hz is incorrect. This does not correspond to the fundamental frequency.
## LEARNING AIDS
	**Common Mistakes**:
		1.[Error 1]: Using the formula for an open pipe. [How to avoid]: Remember the different wavelength relationships for open and closed pipes.
		2.[Error 2]: Forgetting to multiply by 4 when calculating the wavelength. [How to avoid]: Visualize the wave in a closed pipe and recall that the length corresponds to a quarter of the fundamental wavelength.
	**Quick Tips**:
		1.[Helpful shortcut]: Use $f = \frac{v}{4L}$ directly for the fundamental frequency of a closed pipe.
		2.[Memory aid]: Remember a closed pipe has a node at the closed end and an antinode at the open end.

Mr. ANIL KUMAR.G · Answer

The correct Option is "$2\,\,Hz$"

Mr. ANIL KUMAR.G · Answer

$4\,\,Hz$

Mr. ANIL KUMAR.G · Answer

$7\,\,Hz$

Mr. ANIL KUMAR.G · Answer

$9\,\,Hz$

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