When source and detector are stationary but the wind is blowing at speed `v_W`, the apparent wavelength `lamda'` on the wind side is related to actual wavelength `lamda` by [take speed of sound is air as v]

Options

A. `lamda'=lamda`
B. `lamda'=(v_W)/(v)lamda`
C. `lamda'=(v_W+v)/(v)lamda`
D. `lamda'=(v)/(v-v_W)lamda`

Explanation

To find the relationship between the apparent wavelength \(\lambda'\) on the wind side and the actual wavelength \(\lambda\) when the source and detector are stationary, but wind is blowing at speed \(v_W\), we can follow these steps:

### Step-by-Step Solution:

1. **Understanding the Situation**:
- The source of sound and the detector are both stationary.
- The wind is blowing at speed \(v_W\) in the direction of the sound wave.

2. **Using the Wave Equation**:
- The speed of sound in air is denoted as \(v\).
- The relationship between speed, frequency, and wavelength is given by the equation:
\[ v = f \lambda \]
- Here, \(f\) is the frequency of the sound wave, and \(\lambda\) is the actual wavelength.

3. **Considering the Effect of Wind**:
- Since the wind is blowing in the same direction as the sound, the effective speed of sound becomes:
\[ v + v_W \]
- This is because the wind adds to the speed of sound.

4. **Relating Apparent Wavelength to Actual Wavelength**:
- The apparent wavelength \(\lambda'\) can be expressed in terms of the effective speed of sound and frequency:
\[ v + v_W = f \lambda' \]
- Rearranging this gives:
\[ \lambda' = \frac{v + v_W}{f} \]

5. **Expressing Frequency in Terms of Actual Wavelength**:
- From the original wave equation, we can express frequency \(f\) as:
\[ f = \frac{v}{\lambda} \]
- Substituting this expression for \(f\) into the equation for \(\lambda'\):
\[ \lambda' = \frac{v + v_W}{\frac{v}{\lambda}} = \frac{(v + v_W) \lambda}{v} \]

6. **Final Relationship**:
- Thus, we can conclude that the relationship between the apparent wavelength \(\lambda'\) and the actual wavelength \(\lambda\) is:
\[ \lambda' = \left(1 + \frac{v_W}{v}\right) \lambda \]