In the case of sound waves, wind a blowing from source to reciver with speed `U_(W)`. Both source and receiver are stationary.If `lambda_(0)` is the original wavelength with no wind and `V` is speed of sound in air then wavelength as received is given by :

Options

A. `lambda_(0)`
B. `((V + U_(W))/(V))lambda_(0)`
C. `((V - U_(W))/(V))lambda_(0)`
D. `((V)/(V + V_(W)))lambda_(0)`

Answer

To solve the problem, we need to determine the wavelength of sound waves received when there is wind blowing from the source to the receiver. Let's break down the solution step by step.

### Step-by-Step Solution

1. **Understand the scenario**:
- We have sound waves emitted from a stationary source.
- There is a wind blowing towards the receiver with speed \( U_W \).
- The speed of sound in air is \( V \).
- The original wavelength without wind is \( \lambda_0 \).

2. **Write the relationship for wavelength without wind**:
- The speed of sound \( V \) is related to the wavelength \( \lambda_0 \) and frequency \( f \) by the equation:
\[ V = f \cdot \lambda_0 \]
- This is our **Equation 1**.

3. **Consider the effect of wind**:
- When the wind is blowing from the source to the receiver, the effective speed of sound becomes \( V + U_W \).
- The new wavelength received, denoted as \( \lambda' \), can be expressed in terms of frequency and effective speed:
\[ V + U_W = f \cdot \lambda' \]
- This is our **Equation 2**.

4. **Relate the two equations**:
- From Equation 1, we can express frequency \( f \) as:
\[ f = \frac{V}{\lambda_0} \]
- Substitute this expression for \( f \) into Equation 2:
\[ V + U_W = \left(\frac{V}{\lambda_0}\right) \cdot \lambda' \]

5. **Rearranging the equation**:
- Rearranging gives:
\[ \lambda' = \frac{(V + U_W) \cdot \lambda_0}{V} \]

6. **Final expression for the received wavelength**:
- Thus, the wavelength as received \( \lambda' \) is given by:
\[ \lambda' = \lambda_0 \cdot \left(1 + \frac{U_W}{V}\right) \]

### Final Answer
The wavelength as received is:
\[ \lambda' = \lambda_0 \cdot \left(1 + \frac{U_W}{V}\right) \]