Assertion: Wave speeds is given by `v=flambda`. If frequency `f` is doubled, `v` will becomes two times.
Reason : For given conditions of medium wave speed remains constant.

Options

A. If both Assertion and Reason are true and the Reason is correct expanation of the Assertion.
B. If both Assertion and Reason are true but the Reason is not correct expanation of the Assertion.
C. If Assertion is true, but the Reason is false.
D. If Assertion 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 wave speed is given by the formula:
\[ v = f \lambda \]
where:
- \( v \) is the wave speed,
- \( f \) is the frequency, and
- \( \lambda \) is the wavelength.

### Step 2: Analyze the Effect of Doubling Frequency
If the frequency \( f \) is doubled, we can denote the new frequency as \( f' = 2f \).

Using the wave speed formula:
\[ v = f \lambda \]
If we double the frequency, we need to consider how the wavelength changes.

### Step 3: Determine the Change in Wavelength
From the wave speed equation, if the frequency is doubled, we can express the new wave speed as:
\[ v' = f' \lambda' = (2f) \lambda' \]

To maintain the wave speed constant (as stated in the reason), the wavelength must change. Since wave speed remains constant for a given medium, we can set the original wave speed equal to the new wave speed:
\[ f \lambda = 2f \lambda' \]

### Step 4: Solve for the New Wavelength
Now, we can rearrange the equation:
\[ \lambda' = \frac{\lambda}{2} \]

This shows that if the frequency is doubled, the wavelength is halved.

### Step 5: Conclusion About Wave Speed
Since the wave speed \( v \) remains constant (as stated in the reason), we conclude that:
\[ v = f \lambda = 2f \left(\frac{\lambda}{2}\right) \]
Thus, the wave speed does not change, and it remains constant regardless of the changes in frequency and wavelength.

### Final Evaluation of Assertion and Reason
- **Assertion**: "If frequency \( f \) is doubled, \( v \) will become two times." This is **false** because the wave speed remains constant.
- **Reason**: "For given conditions of medium, wave speed remains constant." This is **true**.

### Final Answer
The assertion is false, and the reason is true. Therefore, the correct option is option number 4.

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