A police car horn emits a sound at a frequency 240 Hz. When the car is at rest. If the speed of the sound is 330 m/s the frequency heard by an observer who is approching the car at a speed of 11 m/s is

Options

A. 248 Hz
B. 244Hz
C. 240 Hz
D. 230 Hz

Explanation

To solve the problem of finding the frequency heard by an observer approaching a police car emitting a sound at a frequency of 240 Hz, 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 source (police car horn), \( f_0 = 240 \, \text{Hz} \)
- Speed of sound in air, \( v = 330 \, \text{m/s} \)
- Speed of the observer (approaching the source), \( v_o = 11 \, \text{m/s} \)
- Speed of the source (police car), \( v_s = 0 \, \text{m/s} \) (since the car is at rest)

### Step 2: Write the Doppler effect formula
The formula for the observed frequency \( f \) when the source is stationary and the observer is moving towards the source is given by:
\[ f = f_0 \left( \frac{v + v_o}{v - v_s} \right) \]
Where:
- \( f \) is the frequency heard by the observer.
- \( f_0 \) is the emitted frequency of the source.
- \( v \) is the speed of sound.
- \( v_o \) is the speed of the observer towards the source.
- \( v_s \) is the speed of the source (which is zero in this case).

### Step 3: Substitute the values into the formula
Substituting the known values into the formula:
\[ f = 240 \left( \frac{330 + 11}{330 - 0} \right) \]

### Step 4: Simplify the equation
Calculating the numerator and denominator:
\[ f = 240 \left( \frac{341}{330} \right) \]

### Step 5: Calculate the observed frequency
Now, perform the multiplication:
\[ f = 240 \times \frac{341}{330} \]
Calculating this gives:
\[ f = 240 \times 1.034 \]
\[ f \approx 248.16 \, \text{Hz} \]

### Step 6: Round to the nearest whole number
Since frequency is typically expressed in whole numbers, we round it:
\[ f \approx 248 \, \text{Hz} \]

### Conclusion
The frequency heard by the observer who is approaching the police car is approximately **248 Hz**.

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