If source and observer both are relatively at rest and if speed of sound is increased then frequency heard by observer will

Options

A. Increases
B. Decreases
C. Can not be predicted
D. Will not change

Answer

To solve the problem, we need to analyze the situation where both the source of sound and the observer are at rest, and we are interested in how the frequency heard by the observer changes when the speed of sound in the medium increases.

### Step-by-Step Solution:

1. **Identify the Given Information:**
- The source of sound and the observer are both at rest.
- The speed of sound in the medium is increased.

2. **Understand the Concept of Frequency:**
- The frequency emitted by the source is denoted as \( f_0 \).
- When both the source and observer are at rest, the frequency heard by the observer is equal to the frequency emitted by the source, which is \( f = f_0 \).

3. **Apply the Doppler Effect Formula:**
- The formula for the apparent frequency \( f \) when the source and observer are at rest is:
\[ f = f_0 \cdot \frac{v}{v} = f_0 \]
- Here, \( v \) is the speed of sound in the medium. Since both the source and observer are at rest, their velocities are zero, and the formula simplifies to \( f = f_0 \).

4. **Analyze the Effect of Increasing Speed of Sound:**
- If the speed of sound \( v \) increases, the formula still holds:
\[ f = f_0 \]
- The apparent frequency \( f \) remains equal to the emitted frequency \( f_0 \) because the velocities of the source and observer do not change.

5. **Conclusion:**
- Therefore, even if the speed of sound in the medium increases, the frequency heard by the observer does not change. The frequency remains \( f_0 \).

### Final Answer:
The frequency heard by the observer will remain the same, which is \( f_0 \).