A locomotive engine approaches a railway station and whistles at a frequency of $400\text{ Hz}$. A…
A locomotive engine approaches a railway station and whistles at a frequency of $400\text{ Hz}$. A stationary observer on the platform observes a change of $40\text{ Hz}$ as the engine passes across him. If the velocity of sound is $340\text{ ms}^{-1}$, the speed of the engine is
$34\text{ ms}^{-1}$
$40\text{ ms}^{-1}$
$17\text{ ms}^{-1}$
$20\text{ ms}^{-1}$
Solution
Given, $f_1 - f_2 = 40$
or $f \left(\frac{340}{340 - v_s}\right) - f \left(\frac{340}{340 + v_s}\right) = 40$
or $400 \left(\frac{340}{340 - v_s}\right) - 400 \left(\frac{340}{340 + v_s}\right) = 40$
Applying Binomial theorem and then solving, we get
$v_s \approx 17\text{ ms}^{-1}$