The concept required to solve this problem is that of the Doppler effect which is defined as the change in frequency of a wave in relation to an observer who is moving relative to the wave source
Mathematically it can be expressed as
[tex]\frac{\lambda_0-\lambda_s}{\lambda_s} = \frac{v}{c}[/tex]
Where,
c = Speed of light
[tex]\lambda_0[/tex] = Peak wavelength
[tex]\lambda_s[/tex] = Peak Wavelength observed
Our values are given as,
[tex]v=975000m/s[/tex]
[tex]c = 3*10^8m/s \rightarrow[/tex] Speed of light
[tex]\lambda_s = 1375*10^{-9}m[/tex]
Basically what we should look for is that 'relative' frequency that is emitted when the star moves away so we clear [tex]\lambda_s[/tex]
Replacing we have,
[tex]\frac{\lambda_0-\lambda_s}{\lambda_s} = \frac{v}{c}[/tex]
[tex]\frac{\lambda_0-1375*10^{-9}}{1375*10^{-9}} = \frac{975000}{3*10^8}[/tex]
[tex]\lambda_0 = 1379.46nm[/tex]
Therefore the peak wavelength that is observed when the star is traveling away from the eart to the velocity given is 1379.46nm
