When a source moves away from stationary observer with velocity v then apparent change in frequency is `Deltan_(1)`. When an observer approaches the stationary source with same velocity `v` then change in frequency is `Deltan_(2)` then

Options

A. `Deltan_(1)=Deltan_(2)`
B. `Deltan_(1) gt Deltan_(2)`
C. `Deltan_(1) lt Deltan_(2)`
D. `(Deltan_(1))/(Deltan_(2)) lt 1`

Explanation

To solve the problem of apparent change in frequency when a source moves away from a stationary observer and when an observer approaches a stationary source, we can use the Doppler effect equations.

### Step-by-Step Solution:

1. **Understanding the Scenario**:
- When the source moves away from the observer, the frequency observed by the observer decreases.
- When the observer approaches the stationary source, the frequency observed by the observer increases.

2. **Define Variables**:
- Let \( f_0 \) be the actual frequency of the source.
- Let \( v \) be the velocity of the source or observer.
- Let \( V \) be the speed of sound in air.
- Let \( f_1 \) be the frequency observed when the source is moving away.
- Let \( f_2 \) be the frequency observed when the observer is moving towards the source.

3. **Frequency Change When Source Moves Away**:
- The formula for the frequency observed when the source is moving away is given by:
\[ f_1 = f_0 \left( \frac{V}{V + v} \right) \]
- The change in frequency, \( \Delta n_1 \), is:
\[ \Delta n_1 = f_0 - f_1 = f_0 - f_0 \left( \frac{V}{V + v} \right) = f_0 \left( 1 - \frac{V}{V + v} \right) \]
- Simplifying this gives:
\[ \Delta n_1 = f_0 \left( \frac{v}{V + v} \right) \]

4. **Frequency Change When Observer Approaches**:
- The formula for the frequency observed when the observer is moving towards the source is given by:
\[ f_2 = f_0 \left( \frac{V + v}{V} \right) \]
- The change in frequency, \( \Delta n_2 \), is:
\[ \Delta n_2 = f_2 - f_0 = f_0 \left( \frac{V + v}{V} \right) - f_0 = f_0 \left( \frac{v}{V} \right) \]

5. **Comparing Changes in Frequency**:
- Now we have:
\[ \Delta n_1 = f_0 \left( \frac{v}{V + v} \right) \]
\[ \Delta n_2 = f_0 \left( \frac{v}{V} \right) \]
- To compare \( \Delta n_1 \) and \( \Delta n_2 \):
\[ \Delta n_1 = \frac{v}{V + v} \Delta n_2 \]
- This shows that \( \Delta n_1 < \Delta n_2 \) because \( V + v > V \).

### Conclusion:
When the source moves away from the observer, the change in frequency \( \Delta n_1 \) is less than the change in frequency \( \Delta n_2 \) when the observer approaches the stationary source.

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