Question 515: Waves

Question

Two vehicles, each moving with speed u on the same horizontal straight road, are approaching each other. Wind blows along the road with velocity w. One of these vehicles blows a whistle of frequency f
1
. An observer in the other vehicle hears the frequency of the whistle to be f
2
. The speed of sound in still air is V. The correct statement(s) is(are)

Accepted Answer

Doppler's effect gives
$${f_2} = \left[ {{{v + {u_0}} \over {v - {u_s}}}} \right]{f_1}$$ ..... (1)
Let the wind speed be w and wind moves towards the source in case (i) and towards the observer in case (ii) (see figure).
In the case (i), u
0
, the speed of observer w.r.t. medium considered positive when it moves towards the source is +(u $$-$$ w) and u
s
, the speed of source w.r.t. medium considered positive when it moves towards observer is +(u + w). Substitute these values in equation (1) to get
$${f_2} = \left[ {{{v + (u - w)} \over {v - (u + w)}}} \right]{f_1}$$,
which is greater than f
1
(assuming u > w). In the case (ii), u
0
is +(u + w) and u
s
is +(u $$-$$ w). Substitute these values in equation (1) to get
$${f_2} = \left[ {{{v + (u + w)} \over {v - (u - w)}}} \right]f1$$,
which is again greater than f
1
.

Answer

If the wind blows from the observer to the source, f
2
> f
1
.

Answer

If the wind blows from the source to the observer, f
2
> f
1
.

Answer

If the wind blows from the observer to the source, f
2
< f
1

Answer

If the wind blows from the source to the observer, f
2
< f
1
.

Waves

Choose the correct answer: