Two cars are moving towards each other at the speed of $50 \mathrm{~ms}^{-1}$. If one of the cars blows a…
Two cars are moving towards each other at the speed of $50 \mathrm{~ms}^{-1}$. If one of the cars blows a horn at a frequency of $250 \mathrm{~Hz}$, the wave length of the sound perceived by the driver of the other car is
(Speed of sound in air $=350 \mathrm{~ms}^{-1}$ )
$18.7 \mathrm{~cm}$
$105 \mathrm{~cm}$
$75 \mathrm{~cm}$
$10.5 \mathrm{~cm}$
Solution
Here, both cars are moving towards each other, hence one car is like an observer and another car is like a source.
$\therefore \quad v_s=50 \mathrm{~m} / \mathrm{s} \Rightarrow v_0=-50 \mathrm{~m} / \mathrm{s}$
Frequency of horn blown by the source car,
$v=250 \mathrm{~Hz}$
According to Doppler's effect, frequency heared by another car $v$ ' is given as
$v^{\prime}=\frac{v-v_0}{v-v_s} \times v=\frac{350-(-50)}{350-50} \times 250$
$\therefore(v=$ speed of sound $=350 \mathrm{~m} / \mathrm{s})$
$=\frac{400 \times 250}{300} \Rightarrow v^{\prime}=\frac{100}{3} \mathrm{~Hz}$
Wavelength of heard sound,
$\lambda^{\prime}=\frac{v}{v^{\prime}}$
$=\frac{350}{1000 / 3}=\frac{1050}{1000}=1.05 \mathrm{~m}=105 \mathrm{~cm}$