Answer #38

The correct answer is C. To answer this question you need to know the Doppler shift equation (see figure). Because this question asks about the magnitude only and not direction (positive or negative change in frequency) we do not care about whether the object is moving toward (increase in frequency, Doppler shift is positive) or away (decrease in frequency, Doppler shift is negative) from the observer. We only care about the absolute change.

From the equation we can see that the Doppler shift is directly proportional to the object velocity, and emitting frequency and the cosine of the angle in line from the observer. Hence the combination of these that is the greatest is the answer. B has a higher velocity than A, so A can be eliminated. D has the same velocity and frequency as B but is at a 10 degree angle. We know that the cosine of anything other than 0 degrees will be less than 1 so D can be eliminated. Similarly E can be eliminated since it's shift will similar to D as the velocity is only 2.5 m/s but the frequency is doubled at 10 MHz. Between B and C then we must ask ourselves is a doubling of the velocity from 5m/s in B to 10m/s in C enough to compensate being off by 10 degrees in angle. Suffice to say that we are commonly off by 10 degrees and it doesn't effect the result by 2 fold. In point of fact the cosine of 10 degrees is 0.985 so it is only 1.5% less. Hence answer C will have the greatest magnitude of Doppler Shift.