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EEJ MAIN Physics QUESTION #7049
Question 1
An observer travels at half the speed of light towards a $10 \text{ GHz}$ microwave source. What frequency does the observer measure? (Assume $c = 3 \times 10^8 \text{ ms}^{-1}$)
  • $15.3 \text{ GHz}$
  • $10.1 \text{ GHz}$
  • $12.1 \text{ GHz}$
  • $17.3 \text{ GHz}$✔️
Correct Answer Explanation

Using the Relativistic Doppler Effect formula for an approaching source:

$f' = f \sqrt{\frac{1 + v/c}{1 - v/c}}$

Given $v = 0.5c$:

$f' = 10 \sqrt{\frac{1 + 0.5}{1 - 0.5}} = 10 \sqrt{\frac{1.5}{0.5}} = 10 \sqrt{3} \approx 10 \times 1.732 = 17.32 \text{ GHz}$.