The speed of sound wave in a given medium is

Options

A. directly proportional to its frequency
B. inversely proportional to its frequency
C. directly proportional to the square of its frequency
D. independent of its frequency

Explanation

To solve the question regarding the speed of sound waves in a given medium, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Relationship**: The speed of sound in a medium is given by the formula:
\[ v = f \cdot \lambda \]
where \( v \) is the speed of sound, \( f \) is the frequency, and \( \lambda \) is the wavelength.

2. **Identify Constants in a Given Medium**: In a specific medium, the wavelength (\( \lambda \)) remains constant. This is because the properties of the medium dictate the wavelength of the sound wave traveling through it.

3. **Analyze the Formula**: Since \( \lambda \) is constant for a given medium, we can express the speed of sound as:
\[ v = f \cdot \text{(constant)} \]
This implies that the speed of sound (\( v \)) is directly proportional to the frequency (\( f \)) of the sound wave.

4. **Conclusion**: Therefore, we can conclude that in a given medium, the speed of sound is directly proportional to its frequency. This leads us to select the correct option from the provided choices.

### Final Answer:
The speed of sound wave in a given medium is **directly proportional to its frequency**.

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