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Question #43108

Difficulty: 8/10 | 🟢 Free

The Question

A stationary space station emits two electromagnetic waves simultaneously in the same direction through a vacuum. The waves have frequencies $f_1 = 8.0 \times 10^{14} \text{ Hz}$ and $f_2 = 4.0 \times 10^{14} \text{ Hz}$ . A spacecraft moves away from the station along the direction of wave propagation at a constant speed $v = \frac{3}{5}c$ , where $c$ is the speed of light in vacuum. An onboard detector measures the superposition of the two waves. What is the beat frequency (frequency of the intensity maxima) detected by the spacecraft?

Options

A.
$2.0 \times 10^{14} \text{ Hz}$
B.
$1.6 \times 10^{14} \text{ Hz}$
C.
$3.2 \times 10^{14} \text{ Hz}$
D.
$4.0 \times 10^{14} \text{ Hz}$

Check Your Answer

Correct Answer

Step-by-Step Solution

Explanation

How the Examiner Thinks

Intuition_Breaker

Train your brain to resist "obvious" answers that are designed to deceive your intuition.

Concepts Behind This Question

Spectrum Order and Frequency/Wavelength|Beats and Frequency Difference|Superposition of Non-identical Waves

Why This Question Is Tricky

Common Mistakes

This question tests the student's understanding of the superposition principle applied to electromagnetic waves and the Relativistic Doppler effect.

A common misconception is that 'beats' are exclusively a mechanical wave phenomenon, whereas they arise from the linearity of the wave equation, which governs EM waves as well.

Furthermore, students often incorrectly apply the Galilean Doppler shift formula ( $f' = f(1-v/c)$ ) to light, yielding the trap answer $1.6 \times 10^{14} \text{ Hz}$ , or they mistakenly assume the beat frequency is invariant or only subject to time dilation ( $f' = f/\gamma$ ), yielding $3.2 \times 10^{14} \text{ Hz}$ .

The correct approach requires applying the Relativistic Doppler shift to each frequency component before finding their difference in the observer's frame.

Quick Facts About This Question

Question Information

Subject	Physics
Chapter	Electromagnetic Waves - Class 12
Concept	Spectrum Order and Frequency/Wavelength
Difficulty	8
Cognitive Load	7
Target Solve Time	160 sec
Access	Free