Assertion : In longitudinal wave pressure is maximum at a point where displacement is zero .
Reason : There is a phase difference of `(pi)/(2)` between `y(x,t)` and `Delta P (x, t)` equation in case of longitudinal wave.

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

### Step 1: Understand the Assertion
The assertion states that "In a longitudinal wave, pressure is maximum at a point where displacement is zero."

- In a longitudinal wave, particles of the medium oscillate back and forth in the direction of wave propagation.
- At points where the displacement of the particles is zero, it corresponds to the locations of compression and rarefaction in the wave.
- However, maximum pressure occurs at the points of compression, where the particles are closest together, not where the displacement is zero.

**Conclusion for Assertion**: The assertion is **incorrect**.

### Step 2: Understand the Reason
The reason states that "There is a phase difference of \(\frac{\pi}{2}\) between \(y(x,t)\) and \(\Delta P(x,t)\) in the case of longitudinal waves."

- The displacement \(y(x,t)\) can be represented as \(y(x,t) = A \sin(\omega t - kx)\).
- The pressure variation \(\Delta P(x,t)\) can be represented as \(\Delta P(x,t) = B A k \cos(\omega t - kx)\).
- The cosine function can be rewritten in terms of sine: \(\cos(\theta) = \sin\left(\theta + \frac{\pi}{2}\right)\).
- This indicates that there is indeed a phase difference of \(\frac{\pi}{2}\) between the displacement and pressure.

**Conclusion for Reason**: The reason is **correct**.

### Final Conclusion
- Since the assertion is false and the reason is true, the correct answer is that the assertion is incorrect while the reason is correct.

### Answer:
Assertion is false, Reason is true.

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