The longitudinal wave velocity in fluid

Options

A. A) does not depend on wave length and frequency
B. B) depends on bulk modulus and density
C. C) is given by `sqrt((B)/(rho))`
D. D) All the above

Answer

To solve the question regarding the longitudinal wave velocity in a fluid, we can follow these steps:

### Step 1: Understand the Concept
The velocity of longitudinal waves in a fluid is determined by the properties of the fluid itself, specifically its bulk modulus and density.

### Step 2: Write the Formula
The formula for the velocity (v) of longitudinal waves in a fluid is given by:
\[ v = \sqrt{\frac{B}{\rho}} \]
where:
- \( B \) is the bulk modulus of the fluid,
- \( \rho \) is the density of the fluid.

### Step 3: Analyze the Dependencies
From the formula, we can analyze the dependencies:
- The velocity \( v \) depends on the bulk modulus \( B \) and the density \( \rho \).
- The formula does not include wavelength or frequency, indicating that the wave velocity is independent of these parameters.

### Step 4: Evaluate the Options
Now, we can evaluate the options given in the question:
- **Option A**: It does not depend on wavelength and frequency - **True**.
- **Option B**: It depends on bulk modulus - **True**.
- **Option C**: It depends on density - **True**.
- **Option D**: All the above are correct - **True**.

### Conclusion
Since all the statements regarding the dependencies of the wave velocity are correct, the correct answer is:
**Option D: All the above are correct.**

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