if the speed of a sound source is equal to the speed fo sound and the source is moving away from the observer, then the ratio of apparent frequency to the original frequency is

Options

A. `1:2`
B. `2:1`
C. `1:4`
D. `4:1`

Answer

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

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

Where:
- \( F' \) = apparent frequency
- \( F \) = original frequency
- \( v \) = speed of sound
- \( v_o \) = speed of the observer (which is 0 since the observer is stationary)
- \( v_s \) = speed of the source

### Step-by-Step Solution:

1. **Identify the Variables**:
- Speed of sound \( v = C \)
- Speed of the observer \( v_o = 0 \) (since the observer is stationary)
- Speed of the source \( v_s = C \) (the source is moving away)

2. **Substitute the Values into the Formula**:
\[ F' = F \cdot \frac{C + 0}{C + C} \]

3. **Simplify the Equation**:
\[ F' = F \cdot \frac{C}{2C} \]

4. **Further Simplification**:
\[ F' = F \cdot \frac{1}{2} \]

5. **Express the Ratio of Apparent Frequency to Original Frequency**:
\[ \frac{F'}{F} = \frac{1}{2} \]

6. **Conclusion**:
The ratio of apparent frequency to original frequency is:
\[ \frac{F'}{F} = \frac{1}{2} \]

### Final Answer:
The ratio of apparent frequency to the original frequency is \( 1:2 \).

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