MCAT Physics Question 104: Answer and Explanation

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Question: 104

14. As an officer approaches a student who is studying with his radio playing loudly beside him, he experiences the Doppler effect. Which of the following statements remains true while the officer moves closer to the student?

I. The apparent frequency of the music is increased.

II. The same apparent frequency would be produced if the officer were stationary and the student approached him at the same speed.

III. The apparent velocity of the wave is decreased.

  • A. I only
  • B. II only
  • C. I and III only
  • D. I, II, and III

Correct Answer: A

Explanation:

Here, an observer is moving closer to a stationary source. The applicable version of the Doppler effect equation is

where ν is the velocity of the sound. Because the numerator is greater than the denominator, f′ will be greater than f; therefore, statement I is true. The scenario described in statement II will produce a similar, but not identical, frequency for the officer: the frequency formula would be

The apparent frequency will increase, but the increase will not be exactly the same as if the officer had been moving. Statement III is false because we already know the frequency increases for the officer—a decrease in velocity would be associated with a decrease in frequency.

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