Question

When a source moves away from stationary observer with velocity v then apparent change in frequency is $\Delta n_1$. When an observer approaches the stationary source with same velocity v then change in frequency is $\Delta n_2$ then :

• A. $\Delta n_1=\Delta n_2$
• B. $\Delta n_1>\Delta n_2$
• C. $\Delta n_1<\Delta n_2$
• D. $\Delta n_1=2\Delta n_2$

Answer 1

The correct option is C $\Delta n_1<\Delta n_2$

Using Doppler effect when a source moves away from stationary observer :
Apparent frequency heard $n_1^{\prime }=n_1[\frac{v_s}{v_s+v}]$
So, change in frequency $\Delta n_1=|n_1^{\prime }-n_1|=\frac{v}{v_s+v}$
Using Doppler effect when an observer moves towards the stationary source :
Apparent frequency heard $n_2^{\prime }=n_2[\frac{v_s+v}{v_s}]$
So, change in frequency $\Delta n_2=|n_2^{\prime }-n_2|=\frac{v}{v_s}$
$⟹$ $\Delta n_2>\Delta n_1$