Answer
(a) less than
(b) $0.89$
Work Step by Step
(a) We know that when the star moves toward the Earth, the frequencies of the electromagnetic waves increase. Since the wavelength and frequency are inversely proportional, the measured wavelengths are less than they would be if the stars are at rest relative to us.
(b) We can find the required fraction of the wavelengths as follows:
$\frac{\lambda^{\prime}}{\lambda}=\frac{f}{f^{\prime}}$
But $f^{\prime}=f(1+\frac{u}{c})$
$\implies \frac{\lambda^{\prime}}{\lambda}=\frac{f}{f(1+\frac{u}{c})}$
$\implies \frac{\lambda^{\prime}}{\lambda}=\frac{1}{(1+\frac{u}{c})}$
We plug in the known values to obtain:
$\frac{\lambda^{\prime}}{\lambda}=\frac{1}{1+\frac{37500\times 10^3}{3\times 10^8}}$
$\frac{\lambda^{\prime}}{\lambda}=0.89$
