An ambulance blowing a siren of frequency 700 Hz is moving with a speed of 2m/s towards a vertical wall. The speed of sound is 352 m/s. Then the frequency of the reflected sound as heard by the driver of ambulance would be

Options

A. 692 Hz
B. 695 Hz
C. 700 Hz
D. 708 Hz

Explanation

To solve the problem of finding the frequency of the reflected sound as heard by the driver of the ambulance, we can follow these steps:

### Step 1: Identify the given values
- Frequency of the siren (f₀) = 700 Hz
- Speed of the ambulance (Vs) = 2 m/s (towards the wall)
- Speed of sound (V) = 352 m/s

### Step 2: Calculate the frequency heard by the wall (f')
The wall acts as a stationary observer, while the ambulance is the moving source. We can use the Doppler effect formula for a source moving towards a stationary observer:

\[ f' = f₀ \times \frac{V}{V - Vs} \]

Substituting the known values:

\[ f' = 700 \times \frac{352}{352 - 2} \]
\[ f' = 700 \times \frac{352}{350} \]

### Step 3: Simplify the expression
Calculating the fraction:

\[ f' = 700 \times 1.006 \]
\[ f' \approx 704.2 \text{ Hz} \]

### Step 4: Calculate the frequency of the reflected sound (f'')
Now, the wall reflects this frequency back to the ambulance. The ambulance is now the observer moving towards the wall (which acts as a source emitting frequency f'). We use the Doppler effect formula for an observer moving towards a stationary source:

\[ f'' = f' \times \frac{V + Vs}{V} \]

Substituting the value of f' we calculated:

\[ f'' = 704.2 \times \frac{352 + 2}{352} \]
\[ f'' = 704.2 \times \frac{354}{352} \]

### Step 5: Simplify the expression
Calculating the fraction:

\[ f'' = 704.2 \times 1.00568 \]
\[ f'' \approx 707.1 \text{ Hz} \]

### Final Answer
The frequency of the reflected sound as heard by the driver of the ambulance is approximately **707.1 Hz**.

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