Two car moving in opposite directions approach each other with speed of `22m//s` and `16.5m//s` respectively. The driver of the first car blows a horn having a frequency `400 Hz`. The frequency heard by the driver of the second car is [velocity of sound `340m//s`].

Options

A. 350HZ
B. 361HZ
C. 411HZ
D. 448HZ

Answer

To solve the problem, we need to find the frequency heard by the driver of the second car when the first car blows its horn. We can use the Doppler effect formula for sound when both the source and observer are moving towards each other.

### Step-by-Step Solution:

1. **Identify the Given Values:**
- Frequency of the horn (f) = 400 Hz
- Speed of sound (V) = 340 m/s
- Speed of the first car (source, V_s) = 22 m/s
- Speed of the second car (observer, V_o) = 16.5 m/s

2. **Doppler Effect Formula:**
When the source and observer are moving towards each other, the frequency heard by the observer (f') can be calculated using the formula:
\[ f' = f \times \frac{V + V_o}{V - V_s} \]
Where:
- \( f' \) = frequency heard by the observer
- \( f \) = frequency of the source
- \( V \) = speed of sound
- \( V_o \) = speed of the observer
- \( V_s \) = speed of the source

3. **Substituting the Values:**
Now, we substitute the known values into the formula:
\[ f' = 400 \times \frac{340 + 16.5}{340 - 22} \]

4. **Calculating the Numerator and Denominator:**
- Numerator: \( 340 + 16.5 = 356.5 \)
- Denominator: \( 340 - 22 = 318 \)

5. **Calculating the Frequency:**
Now plug these values back into the equation:
\[ f' = 400 \times \frac{356.5}{318} \]

6. **Performing the Division:**
\[ \frac{356.5}{318} \approx 1.12 \]

7. **Final Calculation:**
\[ f' \approx 400 \times 1.12 = 448 \text{ Hz} \]

### Conclusion:
The frequency heard by the driver of the second car is approximately **448 Hz**.