Assertion : Fundamental frequency of a narrow pipe is more.
Reason : According to Laplace end correction if radius of pipe is less, frequency should be more.

Options

A. If both Asseration and Reason are true an dthe Reason is correct explanation of the Asseration.
B. If both Asseration and Reason are true but Reason is not the correct explanation of Asseration.
C. If Asseration is true , but the Reason is false.
D. If Asseration is false but the Reason is true.

Explanation

To analyze the given assertion and reason, we will break down the concepts of fundamental frequency in narrow pipes and the implications of Laplace's end correction.

### Step 1: Understand the Assertion
The assertion states that the fundamental frequency of a narrow pipe is more.

- **Fundamental Frequency**: The fundamental frequency (f₀) of a pipe is the lowest frequency at which it can vibrate. For a closed pipe, it is given by the formula:
\[ f_0 = \frac{V}{4L + 0.6R} \]
where \( V \) is the speed of sound, \( L \) is the length of the pipe, and \( R \) is the radius of the pipe.

### Step 2: Analyze the Effect of Pipe Radius
According to the formula, if the radius \( R \) is small (which is the case for a narrow pipe), the term \( 0.6R \) becomes negligible compared to \( 4L \).

- As \( R \) decreases, the denominator \( 4L + 0.6R \) becomes smaller, leading to an increase in the fundamental frequency \( f_0 \).

### Step 3: Understand the Reason
The reason states that according to Laplace's end correction, if the radius of the pipe is less, the frequency should be more.

- **Laplace's End Correction**: This correction accounts for the fact that the effective length of the pipe is slightly longer than its physical length due to the end effects. For a narrow pipe, as the radius decreases, the impact of this correction becomes less significant, thus allowing the frequency to be higher.

### Step 4: Conclusion
Both the assertion and the reason are true. The assertion correctly states that a narrow pipe has a higher fundamental frequency, and the reason correctly explains why this is the case according to Laplace's end correction.

### Final Answer
- **Assertion**: True
- **Reason**: True
- **Explanation**: The reason is a correct explanation for the assertion.