A car moving with a speed of `30 ms^(-1)` is approaching a factory whistle having the frequency 700 Hz. Calculate the apparent pitch of the whistle as heard by the driver of the car ? (Velocity of sound = 350m/s)

Answer

To solve the problem of finding the apparent pitch of the whistle as heard by the driver of the car, we will use the Doppler effect formula for sound. The formula for the apparent frequency \( f' \) when the source is stationary and the observer is moving towards the source is given by:

\[ f' = f \frac{V + V_0}{V} \]

Where:
- \( f' \) = apparent frequency (what the driver hears)
- \( f \) = actual frequency of the source (700 Hz)
- \( V \) = speed of sound (350 m/s)
- \( V_0 \) = speed of the observer (the car) towards the source (30 m/s)

### Step 1: Identify the values
- Actual frequency \( f = 700 \, \text{Hz} \)
- Speed of sound \( V = 350 \, \text{m/s} \)
- Speed of the observer \( V_0 = 30 \, \text{m/s} \)

### Step 2: Substitute the values into the formula
Substituting the values into the Doppler effect formula:

\[ f' = 700 \, \text{Hz} \times \frac{350 \, \text{m/s} + 30 \, \text{m/s}}{350 \, \text{m/s}} \]

### Step 3: Calculate the numerator
Calculate the numerator:

\[ 350 \, \text{m/s} + 30 \, \text{m/s} = 380 \, \text{m/s} \]

### Step 4: Substitute back into the equation
Now substitute back into the equation:

\[ f' = 700 \, \text{Hz} \times \frac{380 \, \text{m/s}}{350 \, \text{m/s}} \]

### Step 5: Simplify the fraction
Now simplify the fraction:

\[ f' = 700 \, \text{Hz} \times \frac{380}{350} \]

### Step 6: Calculate the apparent frequency
Now calculate \( f' \):

\[ f' = 700 \, \text{Hz} \times 1.0857 \approx 760 \, \text{Hz} \]

### Final Answer
Thus, the apparent pitch of the whistle as heard by the driver of the car is approximately \( 760 \, \text{Hz} \).

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