Question
Two cars moving in opposite directions approach each other with speed of $$22\,m/s$$ and $$16.5\,m/s$$ respectively. The driver of the first car blows a horn having a frequency $$400\,Hz.$$ The frequency heard by the driver of the second car is [velocity of sound $$340\,m/s$$ ]
A.
$$350\,Hz$$
B.
$$361\,Hz$$
C.
$$411\,Hz$$
D.
$$448\,Hz$$
Answer :
$$448\,Hz$$
Solution :
When both source and observer are moving towards each other, apparent frequency is given by
$${f_a} = {f_0}\left( {\frac{{v + {v_0}}}{{v - {v_s}}}} \right)$$
where,
$${{f_0}} = $$ original frequency of source
$${{v_s}} = $$ speed of source
$${{v_0}} = $$ speed of observer
$$v = $$ speed of sound
Frequency of the horn,
$${f_0} = 400\,Hz$$
Speed of observer in the second car,
$${v_0} = 16.5\,m/s$$
Speed of source,
$$\eqalign{ & {v_s} = {\text{speed of first car}} \cr & = 22\,m/s \cr} $$
Frequency heard by the driver in the second car
$$\eqalign{ & {f_a} = {f_0}\left( {\frac{{v + {v_0}}}{{v - {v_s}}}} \right) = 400\left( {\frac{{340 + 16.5}}{{340 - 22}}} \right) \cr & = 448\,Hz \cr} $$
When both source and observer are moving towards each other, apparent frequency is given by
$${f_a} = {f_0}\left( {\frac{{v + {v_0}}}{{v - {v_s}}}} \right)$$
where,
$${{f_0}} = $$ original frequency of source
$${{v_s}} = $$ speed of source
$${{v_0}} = $$ speed of observer
$$v = $$ speed of sound
Frequency of the horn,
$${f_0} = 400\,Hz$$
Speed of observer in the second car,
$${v_0} = 16.5\,m/s$$
Speed of source,
$$\eqalign{ & {v_s} = {\text{speed of first car}} \cr & = 22\,m/s \cr} $$
Frequency heard by the driver in the second car
$$\eqalign{ & {f_a} = {f_0}\left( {\frac{{v + {v_0}}}{{v - {v_s}}}} \right) = 400\left( {\frac{{340 + 16.5}}{{340 - 22}}} \right) \cr & = 448\,Hz \cr} $$