Sound waves of length `lamda` travelling with velocity v in a medium enter into another medium in which their velocity is 4v. The wavelength in 2nd medium is:

Options

A. `4 lamda`
B. `lamda`
C. `lamda//4`
D. `16 lamda`

Explanation

To solve the problem of finding the wavelength of sound waves in a second medium where the velocity is different, we can follow these steps:

### Step-by-Step Solution:

1. **Identify Given Values**:
- Wavelength in the first medium: \( \lambda \)
- Velocity in the first medium: \( v \)
- Velocity in the second medium: \( 4v \)

2. **Understand the Relationship Between Velocity, Frequency, and Wavelength**:
- The relationship is given by the formula:
\[ v = f \lambda \]
- Here, \( f \) is the frequency of the sound wave.

3. **Set Up the Equation for the First Medium**:
- For the first medium, we can write:
\[ v = f \lambda \quad \text{(Equation 1)} \]

4. **Set Up the Equation for the Second Medium**:
- In the second medium, the velocity is \( 4v \) and the wavelength is \( \lambda_2 \). Thus, we can write:
\[ 4v = f \lambda_2 \quad \text{(Equation 2)} \]

5. **Relate the Two Equations**:
- Since the frequency \( f \) remains constant when the wave moves from one medium to another, we can divide Equation 1 by Equation 2:
\[ \frac{v}{4v} = \frac{f \lambda}{f \lambda_2} \]
- This simplifies to:
\[ \frac{1}{4} = \frac{\lambda}{\lambda_2} \]

6. **Solve for \( \lambda_2 \)**:
- Rearranging the equation gives:
\[ \lambda_2 = 4 \lambda \]

### Final Answer:
The wavelength in the second medium is \( \lambda_2 = 4\lambda \).

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