The bulk modulus and the density of water are greater than those of air. With this much of information, we can say that velocity of sound in air

Options

A. is larger than its value in water
B. is smaler than its value in water
C. is equal to its value in water
D. cannot be compared with its value inn water.

Answer

To determine the velocity of sound in air based on the given information about the bulk modulus and density of water and air, we can follow these steps:

### Step 1: Understand the relationship between velocity of sound, bulk modulus, and density
The velocity of sound \( v \) in a medium is given by the formula:
\[ v = \sqrt{\frac{B}{\rho}} \]
where \( B \) is the bulk modulus and \( \rho \) is the density of the medium.

### Step 2: Analyze the given information
We know that:
- The bulk modulus of water (\( B_{water} \)) is greater than that of air (\( B_{air} \)).
- The density of water (\( \rho_{water} \)) is greater than that of air (\( \rho_{air} \)).

### Step 3: Compare the ratios of bulk modulus to density
To compare the velocities of sound in air and water, we need to look at the ratio \( \frac{B}{\rho} \) for both media:
- For water: \( \frac{B_{water}}{\rho_{water}} \)
- For air: \( \frac{B_{air}}{\rho_{air}} \)

### Step 4: Determine if we can compare the two ratios
Although we know that \( B_{water} > B_{air} \) and \( \rho_{water} > \rho_{air} \), we do not have specific values for these quantities. Therefore, we cannot definitively conclude whether:
\[ \frac{B_{water}}{\rho_{water}} >, <, \text{ or } = \frac{B_{air}}{\rho_{air}} \]
This means we cannot determine the velocity of sound in air relative to that in water.

### Step 5: Conclusion
Based on the analysis, we conclude that with the information provided, the velocity of sound in air cannot be compared with its value in water. Thus, the correct answer is that the velocity of sound in air is "cannot be compared" with that in water.

### Final Answer
The velocity of sound in air cannot be compared with that in water.

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