A `300 H_(Z)` source, an observer and a wind are moving as shows in the figure with respect to the ground. What frequency is heard by observer ? Take speed of sound in air = `340 m//s` .
`underset(20m//s)overset(observer)(larr)` `underset(rarr)(rarr)5 m//s` `underset(10m//s)overset(source)(rarr)`

Explanation

To find the frequency heard by the observer, we can use the Doppler effect formula for sound. The formula for the observed frequency \( f' \) when both the source and observer are moving, and considering the wind speed, is given by:

\[ f' = f \cdot \frac{V - V_w - V_o}{V - V_w + V_s} \]

Where:
- \( f \) = frequency of the source (300 Hz)
- \( V \) = speed of sound in air (340 m/s)
- \( V_w \) = speed of wind (5 m/s)
- \( V_o \) = speed of observer (20 m/s)
- \( V_s \) = speed of source (10 m/s)

### Step 1: Identify the parameters
- Frequency of the source, \( f = 300 \, \text{Hz} \)
- Speed of sound, \( V = 340 \, \text{m/s} \)
- Speed of wind, \( V_w = 5 \, \text{m/s} \)
- Speed of observer, \( V_o = 20 \, \text{m/s} \)
- Speed of source, \( V_s = 10 \, \text{m/s} \)

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

\[ f' = 300 \cdot \frac{340 - 5 - 20}{340 - 5 + 10} \]

### Step 3: Simplify the numerator and denominator
Calculate the numerator:

\[ 340 - 5 - 20 = 315 \]

Calculate the denominator:

\[ 340 - 5 + 10 = 345 \]

### Step 4: Substitute the simplified values back into the formula
Now, substitute the simplified values back into the formula:

\[ f' = 300 \cdot \frac{315}{345} \]

### Step 5: Calculate the observed frequency
Now calculate \( f' \):

\[ f' = 300 \cdot 0.913 \]

Calculating this gives:

\[ f' \approx 273.33 \, \text{Hz} \]

### Final Result
The frequency heard by the observer is approximately \( 273.33 \, \text{Hz} \).