Assertion : The fundamental frequency of a stretched string is directly proportional to the square root of the tension in the string if length and mass of the string are constant.
Reason : There are n nodes and n antinodes forms when standing waves are formed in a stretched string.

Options

A. If both assertion and reason are correct and reason is a correct explanation of the assertion.
B. If both assertion and reason are correct but reason is not the correct explanation of assertion.
C. If assertion is correct but reason is incorrect
D. If assertion is incorrect but reason is correct.

Answer

To solve the problem, we need to analyze both the assertion and the reason provided in the question.

### Step 1: Analyze the Assertion
The assertion states that "The fundamental frequency of a stretched string is directly proportional to the square root of the tension in the string if length and mass of the string are constant."

- The formula for the fundamental frequency (f) of a stretched string is given by:
\[ f = \frac{1}{2L} \sqrt{\frac{T}{\mu}} \]
where:
- \( L \) = length of the string,
- \( T \) = tension in the string,
- \( \mu \) = mass per unit length of the string.

- If the length (L) and mass per unit length (μ) are constant, we can see that the frequency is directly proportional to the square root of the tension (T):
\[ f \propto \sqrt{T} \]
- Therefore, the assertion is **correct**.

### Step 2: Analyze the Reason
The reason states that "There are n nodes and n antinodes formed when standing waves are formed in a stretched string."

- In a standing wave, the number of nodes (N) and antinodes (A) is related to the harmonic number (n). For the nth harmonic:
- There are \( n \) antinodes and \( n + 1 \) nodes.

- Therefore, the statement that there are "n nodes and n antinodes" is incorrect. It should be "n nodes and n + 1 antinodes" for the nth harmonic.

### Conclusion
- The assertion is correct, but the reason is incorrect. Therefore, the answer to the question is that the assertion is true, but the reason is false.

### Final Answer
- Assertion: True
- Reason: False

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