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 need to find the speed of the car based on the frequency of the sound emitted and the frequency of the sound observed after reflection from the wall.

### Step-by-Step Solution:

1. **Identify the Given Values:**
- Frequency of the horn (source frequency), \( f_0 = 440 \, \text{Hz} \)
- Frequency of the reflected sound (observed frequency), \( f' = 480 \, \text{Hz} \)
- Speed of sound in air, \( V = 350 \, \text{m/s} \)

2. **Use the Doppler Effect Formula:**
When the source of sound is moving towards a stationary observer (the wall), the frequency observed by the observer can be calculated using the formula:
\[ f' = f_0 \frac{V + V_o}{V - V_s} \]
where:
- \( V \) = speed of sound
- \( V_o \) = speed of the observer (the car)
- \( V_s \) = speed of the source (the car)

In this case, since the wall is stationary, \( V_s = V_o \).

3. **Substituting Values:**
The car is moving towards the wall, so we can substitute \( V_s = V_o \):
\[ f' = f_0 \frac{V + V_o}{V - V_o} \]
Plugging in the known values:
\[ 480 = 440 \frac{350 + V_o}{350 - V_o} \]

4. **Cross-Multiplying to Solve for \( V_o \):**
\[ 480(350 - V_o) = 440(350 + V_o) \]
Expanding both sides:
\[ 168000 - 480V_o = 154000 + 440V_o \]

5. **Rearranging the Equation:**
Combine like terms:
\[ 168000 - 154000 = 480V_o + 440V_o \]
\[ 14000 = 920V_o \]

6. **Solving for \( V_o \):**
\[ V_o = \frac{14000}{920} \approx 15.217 \, \text{m/s} \]

7. **Convert \( V_o \) to km/hr:**
To convert from meters per second to kilometers per hour, multiply by \( \frac{18}{5} \):
\[ V_o \approx 15.217 \times \frac{18}{5} \approx 54.78 \, \text{km/hr} \]

### Final Answer:
The speed of the car is approximately \( 54.78 \, \text{km/hr} \).