Two aeroplanes are moving towards each other and cross each other. Then the apparent pitch

Options

A. first decreases and after crossing it increases
B. first increases and after crossing it decreases
C. first remains constant and then decreases
D. continuously increases

Answer

To solve the problem regarding the apparent pitch of two aeroplanes moving towards each other, we can follow these steps:

### Step-by-Step Solution

1. **Understanding the Situation**:
- Two aeroplanes are moving towards each other. Let's denote the speed of sound in air as \( v \), the speed of the first aeroplane as \( v_1 \), and the speed of the second aeroplane as \( v_2 \).

2. **Frequency of Sound**:
- The frequency of the sound emitted by the source (aeroplane) is denoted as \( f_0 \).

3. **Apparent Frequency Calculation**:
- When two sources are moving towards each other, the apparent frequency \( f' \) can be calculated using the Doppler effect formula.
- For the observer moving towards the source, the formula is:
\[ f' = f_0 \left( \frac{v + v_o}{v - v_s} \right) \]
- Here, \( v_o \) is the speed of the observer (which can be considered as \( v_2 \) for the second aeroplane) and \( v_s \) is the speed of the source (which can be considered as \( v_1 \) for the first aeroplane).

4. **Applying the Formula**:
- Since both aeroplanes are moving towards each other, we can substitute \( v_o = v_2 \) and \( v_s = v_1 \):
\[ f' = f_0 \left( \frac{v + v_2}{v - v_1} \right) \]

5. **Analyzing the Changes**:
- As both aeroplanes approach each other, the numerator \( (v + v_2) \) increases while the denominator \( (v - v_1) \) decreases.
- This results in an increase in the apparent frequency \( f' \).

6. **Conclusion**:
- Therefore, the apparent pitch (or frequency) of the sound will first increase as they approach each other and then will decrease after they cross each other.