in which of the following case frequency of sound heard by the observer increases?

Options

A. when source are moving away from the stationary observer
B. when observer are moving away from the stationary source
C. when both observer and source are moving away from each other
D. when both observer and source are moving towards each other

Answer

To determine in which case the frequency of sound heard by the observer increases, we can analyze each option based on the Doppler effect.

1. **Case 1: Source moving away from a stationary observer**
- Here, the source emits a frequency \( f_0 \) and moves away from the observer. As the source moves away, the distance between the source and observer increases, leading to a decrease in the frequency heard by the observer.
- **Conclusion**: Frequency decreases. (Option 1 is incorrect)

2. **Case 2: Observer moving away from a stationary source**
- In this scenario, the source is stationary and emits a frequency \( f_0 \), while the observer moves away from the source. As the observer moves away, the distance between the source and observer increases, resulting in a decrease in the frequency heard by the observer.
- **Conclusion**: Frequency decreases. (Option 2 is incorrect)

3. **Case 3: Both source and observer moving away from each other**
- In this case, both the source and the observer are moving away from each other. The source emits a frequency \( f_0 \), and since both are moving away, the relative distance increases, leading to a decrease in the frequency heard by the observer.
- **Conclusion**: Frequency decreases. (Option 3 is incorrect)

4. **Case 4: Both observer and source moving towards each other**
- Here, the source emits a frequency \( f_0 \) and both the observer and the source are moving towards each other. As they approach, the relative distance decreases, which causes the frequency heard by the observer to increase.
- **Conclusion**: Frequency increases. (Option 4 is correct)

Thus, the correct answer is **Option 4: When both observer and source are moving towards each other, the frequency of sound heard by the observer increases.**