A bat moving at 1`0 ms^(-1)` towards a wall sends a sound signal of 8000 Hz towards it. On reflection it hears a sound of frequency f. The value of g in Hz is close to (speed to sound `= 320 ms^(-1)`) :

Options

A. 8258
B. 8424
C. 8000
D. 8516

Answer

To solve the problem, we will use the Doppler effect formula for sound. The bat is moving towards a wall, and we need to calculate the frequency of the sound that it hears after the sound reflects off the wall.

### Step-by-step Solution:

1. **Identify Given Values**:
- Speed of the bat (V_s) = 10 m/s (towards the wall)
- Frequency of the sound emitted by the bat (f₀) = 8000 Hz
- Speed of sound in air (V) = 320 m/s

2. **Apply the Doppler Effect Formula**:
The formula for the apparent frequency (f) heard by the bat after the sound reflects off the wall is given by:
\[ f = f₀ \times \frac{V + V_s}{V - V_s} \]
where:
- \( f₀ \) is the original frequency (8000 Hz),
- \( V \) is the speed of sound (320 m/s),
- \( V_s \) is the speed of the source (10 m/s).

3. **Substitute the Values into the Formula**:
\[ f = 8000 \times \frac{320 + 10}{320 - 10} \]
\[ f = 8000 \times \frac{330}{310} \]

4. **Calculate the Fraction**:
First, calculate \( \frac{330}{310} \):
\[ \frac{330}{310} \approx 1.0645 \]

5. **Multiply by the Original Frequency**:
Now, calculate \( f \):
\[ f \approx 8000 \times 1.0645 \approx 8516 \text{ Hz} \]

6. **Final Answer**:
The frequency that the bat hears after the sound reflects off the wall is approximately **8516 Hz**.