Concept:When a source moves at high speed towards a stationary observer, extreme wave compression occurs, raising the frequency significantly.
Formula:$$ f' = f \left( \frac{v}{v - v_s} \right) $$
Solution:- Given: True frequency \( f = 200 \text{ Hz} \) and source velocity \( v_s = 0.5v \).
- Substitute into the Doppler equation: \( f' = 200 \left( \frac{v}{v - 0.5v} \right) \).
- Simplify the denominator: \( v - 0.5v = 0.5v \).
- Evaluate the fraction: \( \frac{v}{0.5v} = \frac{1}{0.5} = 2 \).
- Multiply by the true frequency: \( f' = 200 \times 2 = 400 \text{ Hz} \).
Why other options are incorrect:Option B (100 Hz) results from incorrectly treating it as a receding source (\( v + 0.5v = 1.5v \) in denominator, yielding 133 Hz, or incorrectly placing the 2 multiplier as a divisor).
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