If the density of air at a point through which a sound wave is passing is maximum at an instant, the pressure at that point will be

Options

A. minimum
B. same as the density of air
C. equal to the atmospheric pressure
D. maximum

Explanation

To solve the question, we need to understand the relationship between density and pressure in the context of sound waves traveling through air. Here’s a step-by-step breakdown:

### Step 1: Understand Sound Waves
Sound waves consist of alternating compressions and rarefactions. In a compression, air molecules are pushed closer together, resulting in a higher density. In a rarefaction, air molecules are spread apart, resulting in a lower density.

**Hint:** Remember that compressions lead to higher density and rarefactions lead to lower density.

### Step 2: Analyze the Given Condition
The question states that the density of air at a point is maximum at a certain instant. This means that we are at a point of compression in the sound wave.

**Hint:** Identify that maximum density corresponds to the compression phase of the sound wave.

### Step 3: Relate Density and Pressure
According to the ideal gas law and the principles of fluid dynamics, pressure is directly proportional to density. This means that when the density of air increases (as in the case of compression), the pressure also increases.

**Hint:** Recall that pressure (P) is directly proportional to density (ρ), so if density increases, pressure must also increase.

### Step 4: Conclusion
Since the density is maximum at the point in question, the pressure at that point will also be maximum. Therefore, the correct answer to the question is that the pressure will be maximum.

**Hint:** Look for the option that states "maximum pressure" as it directly correlates with maximum density.

### Final Answer
The pressure at that point will be maximum.