A listener and a source of sound are moving with the same speed in the same direction. The ratio of the frequency of the source and the frequency which is heard by the listerner is

Options

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

Answer

To solve the problem, we need to determine the ratio of the frequency of the source of sound (F₀) to the frequency heard by the listener (F) when both the source and the listener are moving with the same speed in the same direction.

### Step-by-Step Solution:

1. **Understand the Scenario**:
- Both the listener and the source of sound are moving with the same speed (let's denote this speed as V) in the same direction.
- The actual frequency of the source is denoted as F₀, and the frequency heard by the listener is denoted as F.

2. **Apply the Doppler Effect Formula**:
- According to the Doppler effect, the apparent frequency (F) heard by a listener moving with a velocity (V₀) relative to the source moving with a velocity (Vs) is given by the formula:
\[ F = F₀ \times \frac{C + V₀}{C + Vs} \]
- Here, C is the speed of sound in the medium.

3. **Substitute the Values**:
- Since both the listener and the source are moving at the same speed (V), we can substitute V₀ = V and Vs = V into the formula:
\[ F = F₀ \times \frac{C + V}{C + V} \]

4. **Simplify the Equation**:
- The equation simplifies to:
\[ F = F₀ \times \frac{C + V}{C + V} = F₀ \times 1 = F₀ \]

5. **Determine the Ratio**:
- Now we need to find the ratio of the frequency of the source (F₀) to the frequency heard by the listener (F):
\[ \text{Ratio} = \frac{F₀}{F} = \frac{F₀}{F₀} = 1 \]

6. **Final Result**:
- The ratio of the frequency of the source to the frequency heard by the listener is:
\[ 1:1 \]

### Conclusion:
The ratio of the frequency of the source (F₀) to the frequency heard by the listener (F) is 1:1.

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