Light from an astronomical source is found to be shifted to a frequency one percent lower than had the source been at rest. What relative velocity could cause such a shift? A) 3.0 × 10⁷ m/s moving away from the observer B) 3.0 × 10⁶ m/s moving away from the observer C) 3.0 × 10⁶ m/s moving toward the observer D) 1.5 × 10⁶ m/s moving toward the observer E) 1.5 × 10⁶ m/s moving away from the observer

Question

Quizplus · Accepted Answer

The shift in frequency, known as the Doppler shift, is given by the equation Δf/f = ± v/c, where Δf is the change in frequency, f is the original frequency, v is the velocity of the source relative to the observer, and c is the speed of light. In this case, Δf/f = -0.01, or -1%. Solving for v/c, we get v/c = ±0.01, or ±1%. Multiplying by the speed of light, c, we get v = ±0.01c. Therefore, the relative velocity could be either 1% toward or away from the observer, which corresponds to choices B and E. However, since the question asks for the velocity causing a one percent lower frequency shift, we can eliminate E because a velocity of 1% away from the observer would cause a one percent higher frequency shift. Therefore, the correct answer is B, 3.0 × 10^16 m/s moving away from the observer.

Light from an Astronomical Source Is Found to Be Shifted