A person going away from a factory on his scooter at a speed of 36 km/hr listens to the siren of the factory. If the actual frequency of the siren is 700 Hz and a wind is blowing along the direction of the scooter at 36 km//hr, find the observed frequency heard by the person. (Given speed of sound `= 340 m//s`)

Explanation

To solve the problem, we will use the Doppler effect formula for sound. The formula for the observed frequency \( f' \) when the observer is moving away from a stationary source is given by:

\[ f' = f_0 \left( \frac{v - v_0}{v} \right) \]

where:
- \( f' \) = observed frequency
- \( f_0 \) = actual frequency of the source (700 Hz)
- \( v \) = speed of sound in air (340 m/s + wind speed)
- \( v_0 \) = speed of the observer (scooter speed)

### Step 1: Convert the speeds from km/hr to m/s
The speed of the scooter and wind is given as 36 km/hr. We can convert this to m/s using the conversion factor \( \frac{5}{18} \):

\[ v_0 = 36 \, \text{km/hr} \times \frac{5}{18} = 10 \, \text{m/s} \]

### Step 2: Calculate the effective speed of sound
The wind is blowing in the same direction as the scooter. Therefore, we add the wind speed to the speed of sound:

\[ v = 340 \, \text{m/s} + 10 \, \text{m/s} = 350 \, \text{m/s} \]

### Step 3: Apply the Doppler effect formula
Now we can substitute the values into the Doppler effect formula:

\[ f' = 700 \, \text{Hz} \left( \frac{350 \, \text{m/s} - 10 \, \text{m/s}}{350 \, \text{m/s}} \right) \]

### Step 4: Simplify the expression
Calculating the numerator:

\[ 350 \, \text{m/s} - 10 \, \text{m/s} = 340 \, \text{m/s} \]

Now substituting back into the formula:

\[ f' = 700 \, \text{Hz} \left( \frac{340 \, \text{m/s}}{350 \, \text{m/s}} \right) \]

### Step 5: Calculate the observed frequency
Now we can calculate the observed frequency:

\[ f' = 700 \, \text{Hz} \times \frac{340}{350} = 700 \, \text{Hz} \times 0.9714 \approx 680 \, \text{Hz} \]

### Final Answer
The observed frequency heard by the person is approximately **680 Hz**.