A train approaching a hill at a speed of `40 km//hr` sounds a whistle of frequency `580 Hz` when it is at a distance of `1km` from a hill. A wind with a speed of `40km//hr` is blowing in the direction of motion of the train Find
(i) the frequency of the whistle as heard by an observer on the hill,
(ii) the distance from the hill at which the echo from the hill is heard by the driver and its frequency.
(Velocity of sound in air `= 1, 200 km//hr`)

Explanation

To solve the problem step by step, we will break it down into two parts as specified in the question.

### Part (i): Finding the frequency of the whistle as heard by an observer on the hill.

1. **Identify the given values:**
- Frequency of the whistle, \( n = 580 \, \text{Hz} \)
- Speed of the train, \( v_s = 40 \, \text{km/hr} = \frac{40 \times 1000}{3600} \, \text{m/s} = \frac{100}{9} \, \text{m/s} \approx 11.11 \, \text{m/s} \)
- Speed of sound in air, \( v = 1200 \, \text{km/hr} = \frac{1200 \times 1000}{3600} \, \text{m/s} = \frac{100}{3} \, \text{m/s} \approx 33.33 \, \text{m/s} \)
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