Light waves and sound waves are similar in several respects. For instance, the intensity of light and sound both decrease with the square of the distance from the source to the observer. For light, intensity corresponds to brightness.
Another similarity is the Doppler shift. Just as the pitch of sound goes up or down depending on the motion of the source and the observer, the frequency of light also depends on the speed with which the light source moves towards or away from the observer. For instance, when the source moves towards the observer (or vice versa), the light gets "blue shifted" to a higher frequency. When the source moves away from the observer (or vice versa), the light gets red shifted to a lower frequency. But for light, unlike sound, a Doppler shift also occurs when the source moves at right angles to an imaginary line connecting the source to the observer. This "transverse" Doppler shift always lowers the frequency; the frequency perceived by the observer is lower than the frequency emitted by the source.
These phenomena are illustrated by binary stars, which are actually two separate stars orbiting each other. In figure 1, a star travels counterclockwise in uniform circular motion, and is observed by an astronaut in a spaceship at point W. (This diagram does not include the second star in the binary system.) The total power emitted by the star stays constant, and the average wavelength of its light is 500 nanometers.
Point W is a distance 2R from the center of the circle traced out by the star, where R denotes the circle's radius.
FIGURE 1

1. | As the star moves from 0° to 180°, its brightness as seen by the astronaut at point W decreases by a factor of:

A. | 2

B. | 3

C. | 4

D. | 9

2. | When the star is at 180°, the astronaut perceives its starlight as having an average wavelength of:

A. | 0

B. | less than 500 nm

C. | 500 nm

D. | more than 500 nm

3. | At which point in its orbit is the star's light most blue shifted, according to the astronaut?

A. | 240°

B. | 270°

C. | 300°

D. | 0°

4. | The astronaut moves his spaceship to the center of the circle traced out by the star, and observes the star's brightness and average wavelength. According to his instruments:

A. | the brightness and average wavelength both stay constant.

B. | the brightness stays constant, but the average wavelength varies with time.

C. | the brightness varies with time, but the average wavelength stays constant.

D. | the brightness and average wavelength both vary with time.

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