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$\bullet$ How fast (as a percentage of light speed) would a star haveto be moving so that the frequency of the light we receive fromit is 10.0$\%$ higher than the frequency of the light it is emitting?Would it be moving away from us or toward us? (Assume it ismoving either directly away from us or directly toward us.)

$v=0.095 \mathrm{c}$Since the frequency received from the star is greater than the frequency emitted by the star the star must be moving toward us.

Physics 101 Mechanics

Chapter 12

Mechanical Waves and Sound

Periodic Motion

Mechanical Waves

Sound and Hearing

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So here we consider the frequency of the listener is going to be equal to the square root of the speed of light minus the velocity divided by the speed of light, plus the velocity again, times the frequency of the listener. We know that the frequency so are you or the frequency of the listeners. Essentially, it's going to be equal to 1.10 times the frequency of the source. No, we know that the frequency of the listener is greater than the frequency of the source. Because the star is We know that because rather because we know the frequency of the listener is greater than the frequency of the source. This means that this the star would be moving towards us. So we're going to say that V equals negative times the absolute value of the And of course we know that see, the speed of light is 3.0 times 10 to the eighth meters per second. Now we can say that the frequency of the listener equals the square root of C plus the absolute value the C minus, the absolute value of e times, the frequency of the source and we can find So we can essentially say that C plus the absolute value of the divided by C minus The absolute value of thie equals that ratio 1.10 squared. And so if we wanted to find the absolute value of the this is simply going to be equal to 1.1 squared minus one time, see divided by one plus 1.1 squared and we find that the is going to be equal to 2.85 times 10 to the seventh Amelia's per second. So essentially one full magnitude lower, then the speed of sound and then the speed of light. Mind you, this is the speed of light and a vacuum. So it's going to be one order of magnitude less than the speed of light in a vacuum. This is this number is slightly less when you ah when when light travels through air. But it's close to 3.0 times 10 to the eighth meters per second and again, that final answer 2.85 times, 10 times 10 to the seventh meters per 2nd 1 order of magnitude less than the speed of light. That is the end of the solution. Thank you for watching

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