A train standing at the outer signal of a railway station blows a whistle of frequency 400 Hz in still air. The train begins to move with a speed of 30 `m s^(- 1)` towards the platform. The frequency of the sound heard by an observer standing on the platform is
(Speed of sound in air = 330 m `s^(-1)`)

Options

A. 420 Hz
B. 430 Hz
C. 440 Hz
D. 450 Hz

Explanation

To find the frequency of the sound heard by an observer on the platform when the train is moving towards them, we can use the Doppler effect formula for sound. Here’s the step-by-step solution:

### Step 1: Identify the given values
- Frequency of the whistle (source frequency, \( f \)) = 400 Hz
- Speed of sound in air (\( v \)) = 330 m/s
- Speed of the train (source speed, \( v_s \)) = 30 m/s

### Step 2: Determine the formula to use
Since the source (train) is moving towards a stationary observer (on the platform), we can use the following Doppler effect formula for frequency heard by the observer:

\[ f' = \frac{v}{v - v_s} \cdot f \]

Where:
- \( f' \) = frequency heard by the observer
- \( v \) = speed of sound in air
- \( v_s \) = speed of the source (train)
- \( f \) = frequency of the source (whistle)

### Step 3: Substitute the known values into the formula
Now, we substitute the values into the formula:

\[ f' = \frac{330 \, \text{m/s}}{330 \, \text{m/s} - 30 \, \text{m/s}} \cdot 400 \, \text{Hz} \]

### Step 4: Simplify the expression
Calculate the denominator:

\[ 330 \, \text{m/s} - 30 \, \text{m/s} = 300 \, \text{m/s} \]

Now, substitute this back into the equation:

\[ f' = \frac{330}{300} \cdot 400 \]

### Step 5: Calculate the frequency
Now, calculate \( \frac{330}{300} \):

\[ \frac{330}{300} = 1.1 \]

Now multiply by 400 Hz:

\[ f' = 1.1 \cdot 400 = 440 \, \text{Hz} \]

### Step 6: Conclusion
The frequency of the sound heard by the observer standing on the platform is:

\[ \boxed{440 \, \text{Hz}} \]