An astronaut is approaching the moon. He sends a ratio signal of frequency `5 xx 10^(9) Hz` and find that the frequency shift in echo received is `10^(3) Hz`. Find his speed of approach.

Answer

30 m/s ,

Explanation

If speed of astronaut is v the apparent frequency received in echo is
`n_(ap) = n_(0)((c +v)/(c- v))`
`n_(ap) = n_(0) (1+(v)/(c))n_(0)(1-(v)/(c))^(-1)`
`n_(ap) = n_(0)((1+2v)/(c))`
`n_(ap) -n_(0) = (2n_(0)v)/(c)`
`v = (c(Deltah))/(2n_(0)) = (3xx10^(8) xx10^(3))/(2xx5xx10^(9))` = 30m/s.