Chapter 25, Problem 95A

To determine

To calculate:The frequency of light that the observers will detect.

Answer to Problem 95A

The observed frequency of light is $8.709\times {10}^{12}$ Hz.

Explanation of Solution

Given:

Frequency: $4.5\times {10}^{14}$ Hz

Velocity: $2750$ m/s.

Formula Used:

Formula to calculate the observed frequency is given by,

  $f_{obs}=f\left(1\pm \frac{v}{c}\right)$

Because the movement of stars is towards each other.

Where,

  $f$ : Frequency

  $c$ : Speed of light $\left(3.00\times {10}^8\right)$ m/sec

  $v$ : Velocity

Calculation:

To calculate the observed frequency, write the formula as,

  $f_{obs}=f\left(1\pm \frac{v}{c}\right)$

Because the movement of stars is towards the observer,

  $f_{obs}=f\left(1+\frac{v}{c}\right)$

Substitute all the given values in the above formula,

  $=$ $\left(4.56\times {10}^{14}\right)\times \left(1+\frac{2.75\times {10}^6}{3.00\times {10}^8}\right)$

  $=$ $8.709\times {10}^{12}$ Hz

Conclusion:

Hence, the observed frequency of light is $8.709\times {10}^{12}$ Hz.