A person riding a car moving at `72 km h^-1` sounds a whistle emitting a wave of frequency 1250 Hz. What frequency will be heard by another person standing on the road (a) in front of the car (b) behind the car ? Speed of sound in air `= 340 m s^-1` .

Explanation

To solve the problem of finding the frequency heard by a person standing on the road when a car is moving and emitting a whistle, we will use the Doppler effect formula. Let's break down the solution step by step.

### Given Data:
- Speed of the car (source), \( V_s = 72 \, \text{km/h} = 20 \, \text{m/s} \) (after conversion)
- Frequency of the whistle (source frequency), \( f_0 = 1250 \, \text{Hz} \)
- Speed of sound in air, \( V = 340 \, \text{m/s} \)
- Speed of the observer, \( V_o = 0 \, \text{m/s} \) (since the observer is standing still)

### Doppler Effect Formula:
The apparent frequency \( f \) heard by the observer can be calculated using the formula:
\[ f = f_0 \left( \frac{V + V_o}{V - V_s} \right) \]
Where:
- \( f_0 \) = original frequency
- \( V \) = speed of sound
- \( V_o \) = speed of the observer
- \( V_s \) = speed of the source

### Part (a): Frequency heard by the person in front of the car
1. **Identify the direction**: The car is moving towards the observer, so the source velocity \( V_s \) is positive.
2. **Substitute values into the formula**:
\[ f_1 = 1250 \left( \frac{340 + 0}{340 - 20} \right) \]
3. **Calculate the denominator**:
\[ 340 - 20 = 320 \]
4. **Calculate the fraction**:
\[ \frac{340}{320} = 1.0625 \]
5. **Calculate the apparent frequency**:
\[ f_1 = 1250 \times 1.0625 = 1328.125 \, \text{Hz} \]

### Part (b): Frequency heard by the person behind the car
1. **Identify the direction**: The car is moving away from the observer, so the source velocity \( V_s \) is negative.
2. **Substitute values into the formula**:
\[ f_2 = 1250 \left( \frac{340 + 0}{340 + 20} \right) \]
3. **Calculate the denominator**:
\[ 340 + 20 = 360 \]
4. **Calculate the fraction**:
\[ \frac{340}{360} = 0.9444 \]
5. **Calculate the apparent frequency**:
\[ f_2 = 1250 \times 0.9444 = 1180.56 \, \text{Hz} \]

### Final Answers:
- (a) The frequency heard by the person in front of the car is approximately **1328.12 Hz**.
- (b) The frequency heard by the person behind the car is approximately **1180.56 Hz**.