Question

Two cars moving in opposite directions approach each other with speeds of $40{\text{ms}}^{-1}$ and $50{\text{ms}}^{-1}$ respectively. The driver of the first car blows a horn of frequency $400\text{Hz}$. The frequency heard by the driver of the second car is
[speed of sound $=340{\text{ms}}^{-1}$]

• A. $515\text{Hz}$
• B. $375\text{Hz}$
• C. $520\text{Hz}$
• D. $450\text{Hz}$

Answer 1

The correct option is C $520\text{Hz}$

From Doppler's effect, the apparent frequency heard by the observer is,
$f^{{}^{\prime }}=f_0\left(\frac{v\pm v_0}{v\pm v_s}\right)$, here,
$f_0$ is the original frequency produced by the source, $v$ is the speed of sound, $v_0$ is the speed of observer and $v_s$ is the speed of source.
$\Rightarrow f^{{}^{\prime }}=400\times \left(\frac{340+50}{340-40}\right)$
$\Rightarrow f^{{}^{\prime }}=520\text{Hz}$