A car is moving towards a fixed wall, it blows form of frequency of `440 Hz` . The frequency of reflected sound observed by the driver is `480 Hz` then find the speed of car in km/hr. (Speed of sound is `350 m/sec`

Options

A. `64.78 km/hr`
B. 26.778 km/hr`
C. `54.78 km/hr`
D. `47.78 km/hr`

Answer

To solve the problem, we will use the Doppler effect formula for sound. The situation involves a car moving towards a fixed wall, emitting sound waves, and the frequency of the reflected sound observed by the driver.

### Step-by-Step Solution:

1. **Identify Given Values:**
- Frequency of the sound emitted by the car (f) = 440 Hz
- Frequency of the reflected sound observed by the driver (f') = 480 Hz
- Speed of sound (v) = 350 m/s

2. **Use the Doppler Effect Formula:**
When the source of sound (the car) is moving towards a stationary observer (the wall), the frequency observed (f') can be calculated using the formula:
\[ f' = f \frac{v}{v - v_c} \]
where:
- \( v_c \) = speed of the car (source)

Substituting the known values:
\[ 480 = 440 \frac{350}{350 - v_c} \tag{1} \]

3. **Rearranging Equation (1):**
Cross-multiply to eliminate the fraction:
\[ 480(350 - v_c) = 440 \cdot 350 \]
Expanding both sides:
\[ 168000 - 480v_c = 154000 \]

4. **Solve for \( v_c \):**
Rearranging gives:
\[ 168000 - 154000 = 480v_c \]
\[ 14000 = 480v_c \]
\[ v_c = \frac{14000}{480} \approx 29.17 \text{ m/s} \tag{2} \]

5. **Convert Speed to km/hr:**
To convert the speed from m/s to km/hr, use the conversion factor \( \frac{18}{5} \):
\[ v_c \text{ (in km/hr)} = 29.17 \times \frac{18}{5} \approx 105.00 \text{ km/hr} \]

### Final Answer:
The speed of the car is approximately **105.00 km/hr**.