The Question is from neet-physics waves , and it was created by the author NAGA SAI

Question

A closed organ pipe has a fundamental frequency of $f$. If the temperature increases, which of the following is true about the fundamental frequency and speed of sound?

NAGA SAI · Accepted Answer

## CORE INFORMATION
✓ **Answer**: [A]
## CONCEPT FRAMEWORK
	**Primary Concept**: Relationship between temperature, speed of sound, and frequency in closed organ pipes.
	**Related Topics**: Wave propagation, sound waves, temperature effects on sound.
	**Prerequisites**: Understanding of wave properties and equations related to sound.
## SOLUTION PATHWAY
**Given Information**:
		The fundamental frequency of a closed organ pipe is $f$. The speed of sound in air is affected by temperature.
**Method & Steps**:
	1. **Understand the relationship between speed of sound and temperature**.
		Reasoning: The speed of sound $v$ in air can be approximated by the formula:
		$$v = 331.3 + 0.6T$$
		where $T$ is the temperature in degrees Celsius.
		This indicates that as the temperature increases, the speed of sound also increases.
	2. **Apply the relationship of frequency to speed and wavelength**.
		Working: For closed organ pipes, the fundamental frequency is given by:
		$$f = \frac{v}{4L}$$
		where $L$ is the length of the pipe. Since $L$ remains constant, an increase in $v$ leads to an increase in $f$.
	3. **Summarize the effects of temperature increase**.
		Result: As temperature increases, both the speed of sound $v$ and the fundamental frequency $f$ increase.
		Verification: The relationship $f \propto v$ confirms that an increase in the speed of sound correlates with an increase in frequency for a constant length pipe.
## OPTION ANALYSIS
[A] ✓: Both frequency and speed of sound increase due to the increase in temperature.
[B] :x: Frequency increases, speed of sound decreases. Incorrect because both frequency and speed increase.
[C] :x: Frequency decreases, speed of sound increases. Incorrect because frequency cannot decrease with an increase in speed.
[D] :x: Both frequency and speed of sound decrease. Incorrect as both quantities increase with temperature.
## LEARNING AIDS
	**Common Mistakes**:
		1. Confusing the effects of temperature on sound speed: Remember that higher temperature increases sound speed.
		2. Misunderstanding the relationship between frequency and speed in wave equations: Always check the constants involved.
	**Quick Tips**:
		1. Recall that speed of sound increases with temperature when in air.
		2. Remember the fundamental frequency relationship for closed pipes to connect changes in parameters.

NAGA SAI · Answer

The correct Option is "Both frequency and speed of sound increase."

NAGA SAI · Answer

Frequency increases, speed of sound decreases.

NAGA SAI · Answer

Frequency decreases, speed of sound increases.

NAGA SAI · Answer

Both frequency and speed of sound decrease.

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