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  • A locomotive engine approches a railway station and whistles at a frequency of 400 Hz.A stationary observer on the platform observes a change of 40 Hz.as the engine passes across him.If the velocit

A locomotive engine approches a railway station and whistles at a frequency of 400 Hz.A stationary observer on the platform observes a change of 40 Hz.as the engine passes across him.If the velocity of sound is 340 m/s, the speed of the engine is-

Option: 1

34 m/s


Option: 2

40 m/s


Option: 3

17 m/s


Option: 4

20 m/s


Answers (1)

best_answer

\mathrm{\begin{aligned} & f_1-f_2=40, \\ & \quad f\left(\frac{340}{340-v_s}\right)-f\left(\frac{340}{340+v_s}\right)=40 \end{aligned}}

OR

 \mathrm{\begin{aligned} & 400\left(\frac{340}{340-v_s}\right)-400\left(\frac{340}{340+v_s}\right)=40 \\ & \frac{340}{340-v_s}-\frac{340}{340+v_s}=\frac{1}{10} \end{aligned}}

\mathrm{\begin{gathered} \frac{340\left(340+v_s\right)-340\left(340-v_s\right)}{(340)^2-v_s^2}=\frac{1}{10} \\ \frac{(340)^2+340 v_s-(340)^2+340 V_x}{(340)^2-v_s^2}=\frac{1}{10} \\ \frac{680 V_s}{(340)^2-v_s^2}=\frac{1}{40} \\ v_s=17 \mathrm{~m} / \mathrm{s} . \end{gathered}}

 

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Pankaj

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