Two cars moving in opposite directions approach each other with speeds of $22\text{ ms}^{-1}$ and $16…
Two cars moving in opposite directions approach each other with speeds of $22\text{ ms}^{-1}$ and $16.5\text{ ms}^{-1}$, respectively. The driver of the first car blows a horn having a frequency $400\text{ Hz}$. The frequency heard by the driver of the second car is (Take, velocity of sound $= 340\text{ ms}^{-1}$) [NEET 2017]
350 Hz
361 Hz
411 Hz
448 Hz
Solution
When both source and observer are moving towards each other, apparent frequency is given by
$f_a = f_o \left(\frac{v + v_o}{v - v_s}\right)$
where, $f_o =$ original frequency of source $= 400\text{ Hz}$,
$v_s =$ speed of source $= 22\text{ ms}^{-1}$,
$v_o =$ speed of observer $= 16.5\text{ ms}^{-1}$
and $v =$ speed of sound $= 340\text{ ms}^{-1}$.
[A source car moves right at $v_s = 22\text{ ms}^{-1}$ towards an observer car moving left at $v_o = 16.5\text{ ms}^{-1}$.]
Frequency heard by the driver in the second car,
$f_a = f_o \left(\frac{v + v_o}{v - v_s}\right) = 400 \left(\frac{340 + 16.5}{340 - 22}\right)$
$= 448.4\text{ Hz} \approx 448\text{ Hz}$