Question

When observer moves toward stationary source with $v_1$, apparent frequency is $F_1$. When moving away with $v_1$, it is $F_2$. If $F_1/F_2 = 2$, find $V/v_1$.

• A. 3
• B. 2
• C. 1
• D. 4

Hint:

$f_{app}$ increases when the gap between source and observer closes.

Answer 1

The Correct Option is A

Step 1: Understanding the Question:
We use the Doppler Effect formula for a stationary source and a moving observer.

Step 2: Key Formula or Approach:
Apparent frequency \( f' = f \left( \frac{V \pm V_o}{V} \right) \).

Step 3: Detailed Explanation:
1. Moving towards: \( F_1 = f \left( \frac{V + V_1}{V} \right) \).
2. Moving away: \( F_2 = f \left( \frac{V - V_1}{V} \right) \).
Given \( \frac{F_1}{F_2} = 2 \):
\[ \frac{f(V + V_1)/V}{f(V - V_1)/V} = 2 \]
\[ \frac{V + V_1}{V - V_1} = 2 \]
\[ V + V_1 = 2V - 2V_1 \]
\[ 3V_1 = V \implies \frac{V}{V_1} = 3 \]

Step 4: Final Answer:
The ratio \( V/V_1 \) is 3.