A source of sound S is moving with a velocity of `50m//s` towards a stationary observer. The observer measures the frequency of the source as 1000 Hz. What will be the apparent frequency of the source as 1000 Hz. What will be the apparent frequency of the source when it is moving away from the observer after crossing him? The velocity of the sound in the medium is `350m//s`

Options

A. (a)1143Hz
B. (b)857Hz
C. (c)750Hz
D. (d)807Hz

Explanation

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

\[ f' = \frac{v + v_o}{v - v_s} f \]

Where:
- \( f' \) = apparent frequency
- \( f \) = actual frequency of the source
- \( v \) = speed of sound in the medium
- \( v_o \) = speed of the observer (0 m/s since the observer is stationary)
- \( v_s \) = speed of the source

### Step 1: Identify the given values
- Actual frequency \( f = 1000 \, \text{Hz} \)
- Speed of sound \( v = 350 \, \text{m/s} \)
- Speed of the source \( v_s = 50 \, \text{m/s} \)
- Speed of the observer \( v_o = 0 \, \text{m/s} \)

### Step 2: Calculate the apparent frequency when the source is moving towards the observer
Using the formula for the apparent frequency when the source is approaching:

\[ f' = \frac{v + v_o}{v - v_s} f \]

Substituting the values:

\[ f' = \frac{350 + 0}{350 - 50} \times 1000 \]

\[ f' = \frac{350}{300} \times 1000 \]

\[ f' = \frac{7}{6} \times 1000 \]

\[ f' = 1166.67 \, \text{Hz} \]

### Step 3: Calculate the apparent frequency when the source is moving away from the observer
Now, when the source is moving away from the observer, we use the formula:

\[ f' = \frac{v + v_o}{v + v_s} f \]

Substituting the values:

\[ f' = \frac{350 + 0}{350 + 50} \times 1000 \]

\[ f' = \frac{350}{400} \times 1000 \]

\[ f' = \frac{7}{8} \times 1000 \]

\[ f' = 875 \, \text{Hz} \]

### Final Answers
1. The apparent frequency when the source is moving towards the observer is approximately **1166.67 Hz**.
2. The apparent frequency when the source is moving away from the observer is **875 Hz**.