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Chapter 37: 35P (page 1147)

A spaceship, moving away from Earth at a speed of 0.900c, reports back by transmitting at a frequency (measured in the spaceship frame) of 100 MHz. To what frequency must Earth receivers be tuned to receive the report?

Short Answer

Expert verified

The tuning frequency to receive the report on Earth is 22.9 MHz.

Step by step solution

01

Identification of given data

The proper frequency in spaceship frame is fo=100MHz

The speed of spaceship away from earth is v=0.900c

The variation in the frequency of light occurs due to relative movement of source and observer in different frames. It is calculated by the formula for frequency variation.

02

Determination of tuning frequency to receive the report on Earth

The tuning frequency to receive the report on Earth is given as:

f=fo1-vc1+vc

Here, c is the speed of light.

Substitute all the values in the above equation.

f=100MHz1-0.900cc1+0.900ccf=22.9MHz

Therefore, the tuning frequency to receive the report on Earth is 22.9 MHz.

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