A train is travelling at `120kmph` and blows a whistle of frequency `1000Hz` . The frequency of the note heard by a stationary observer if the train is approaching him and moving away from him are (Velocity of sound in air `=330=ms^(-1)`)

Options

A. `1112Hz`, `908Hz`
B. `908Hz`, `1112Hz`
C. `1080Hz`, `820Hz`
D. `820Hz`, `1080Hz`

Explanation

To solve the problem, we will use the Doppler effect formula for sound. The frequency heard by a stationary observer when the source of sound is moving can be calculated using the following formulas:

1. **When the source is approaching the observer:**
\[ f' = f \left( \frac{v + v_o}{v - v_s} \right) \]
where:
- \( f' \) = frequency heard by the observer
- \( f \) = frequency of the source (1000 Hz)
- \( v \) = speed of sound in air (330 m/s)
- \( v_o \) = speed of the observer (0 m/s, since the observer is stationary)
- \( v_s \) = speed of the source (train) in m/s

2. **When the source is moving away from the observer:**
\[ f' = f \left( \frac{v - v_o}{v + v_s} \right) \]

### Step 1: Convert the speed of the train from km/h to m/s
The speed of the train is given as 120 km/h. To convert this to m/s:
\[ v_s = 120 \, \text{km/h} \times \frac{1000 \, \text{m}}{1 \, \text{km}} \times \frac{1 \, \text{h}}{3600 \, \text{s}} = \frac{120000}{3600} = 33.33 \, \text{m/s} \]

### Step 2: Calculate the frequency heard by the observer when the train is approaching
Using the formula for when the source is approaching:
\[ f' = f \left( \frac{v + v_o}{v - v_s} \right) \]
Substituting the values:
\[ f' = 1000 \left( \frac{330 + 0}{330 - 33.33} \right) = 1000 \left( \frac{330}{296.67} \right) \]
Calculating the value:
\[ f' \approx 1000 \times 1.11 \approx 1112.35 \, \text{Hz} \]

### Step 3: Calculate the frequency heard by the observer when the train is moving away
Using the formula for when the source is moving away:
\[ f' = f \left( \frac{v - v_o}{v + v_s} \right) \]
Substituting the values:
\[ f' = 1000 \left( \frac{330 - 0}{330 + 33.33} \right) = 1000 \left( \frac{330}{363.33} \right) \]
Calculating the value:
\[ f' \approx 1000 \times 0.91 \approx 910.00 \, \text{Hz} \]

### Final Results:
- Frequency heard when the train is approaching: **1112.35 Hz**
- Frequency heard when the train is moving away: **910.00 Hz**