question_answer

Two stationary sources each emitting waves of wave length \[\lambda \]. An observer moves from one source to other with velocity u. Then number of beats heared by him:-

A)  \[\frac{2u}{\lambda }\]                            

B)  \[\frac{u}{\lambda }\]

C)  \[\sqrt{u\lambda }\]                     

D)  \[\frac{u}{2\lambda }\]

Correct Answer: A

Solution :

for first source \[{{n}_{1}}=n\left( \frac{v-u}{v} \right)=\left( 1-\frac{u}{v} \right)n\] for II nd source \[{{n}_{2}}=n\left( \frac{v+u}{v} \right)=\left( 1+\frac{u}{v} \right)n\] Beat freq. \[=\left| {{n}_{1}}-{{n}_{2}} \right|=n+\frac{nu}{v}-n+\frac{nu}{v}\] \[=\frac{2nu}{v}=2\frac{u}{\lambda }\]  \[\left[ \because \,\,v=n\lambda \,\,\,\therefore \,\,\frac{1}{\lambda }=\frac{n}{v} \right]\]