Question

Find the diffference is the apparent frequencies (i) When the source approaches a stationary observer (ii) When observer is approaching the stationary source. Take b as relative velocity in each case and `upsilon` as the velocity of the waves.

Answer 1

(i) When source is approaching a stationary observer
`v_(1)=(upsilon.v)/(upsilon-upsilon_(s))=(upsilonv)/(upsilon-b)` …(i)
(ii) When observer is approaching th e stationary source,
`v_(2)=((upsilon+upsilon_(L))v)/(upsilon)=((upsilon+b)v)/(upsilon` ...(ii)
`v_(2)-v_(2)=(upsilonv)/(upsilon-b)-((upsilon+b)v)/(upsilon)`
`=(upsilon^(2)v-(upsilon^(2)-b^(2))v)/((upsilon-b)upsilon)=((upsilon^(2)-upsilon^(*2)+b^(2))v)/(upsilon(upsilon-b))`
`v_(1)-v_(2)=(vb^(2))/(upsilon(upsilon-b))`