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An observer on Earth receives a signal of 6.614 THz. Thirty minutes later, he receives another...

An observer on Earth receives a signal of 6.614 THz. Thirty minutes later, he receives another signal, followed by a third signal 24.331 minutes after the second. The observer on Earth knows that the ship should be sending signals at a 2.500 THz. How far away is the ship from Earth and how often is the captain of the ship sending signals according to her watch?

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Expert Solution

Observed frequency=6.614 THz

source frequency=2.5 THz

The time taken by the signal gets reduced in 2nd instance. This means that ship is moving towards the observer. The velocity of ship can be determined using Doppler effect:

substituting the values, we get

Squaring both sides

Solving this, we get

This is the velocity with which the ship is moving towards the observer. The time after which captain of the ship send signals can be found out using time dilation.

where is the time measured in ship's frame of reference and is called proper time.

Substituting the values, we get

This gives:

This is the time period after which captain of ship sends signal in her frame of reference.

genius_generous answered 2 years ago
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