Physics - Sound Wave Question with Solution | TestHub

Given that the apparent wavelength is $0.02\%$ more than the actual wavelength, the fractional change in wavelength is:

$\frac{\Delta \lambda }{\lambda }=\frac{0.02}{100}=2\times 10^{-4}$

Using the formula for the Doppler effect of light for a star moving away from the earth ($v\ll c$):

$\frac{\Delta \lambda }{\lambda }=\frac{v}{c}$

Substituting the given values:

$2\times 10^{-4}=\frac{v}{3\times 10^8}$

$v=2\times 10^{-4}\times 3\times 10^8$

$v=6\times 10^4\text{ m/s}$

$v=60\times 10^3\text{ m/s}=60\text{ km/s}$

Answer: $60\mathrm{km}/\mathrm{s}$