IIT JEE Advanced 2010 Paper 1

Let car B be the observer (moving towards S).

The frequency observed is f1 = f0(

c+v

c

)
When sound gets reflected, the frequency observed by source S is f2 = f1(

c

c−v

)
where V is the speed of car and C is the speed of sound.
Therefore,
f2 = f0(

c+v

c−v

)
Now, dfx = f0[

(c−v)dv−(c+v)(−dv)

(c−v)2

] =

2f0cdv

(c−v)2

That is,

2f0cdv

(c−v)2

= (

1.2

100

)f0 ⇒ dv =

1.2

100

×

(c−v)2

2c

Since v << c, we get c − v ~ c. Therefore,
dv =

1.2

100

×

c

2

= 1.98 m/s = 1.98 ×

18

5

km/h = 7 km/h