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(C) When the train is approaching,the frequency heard by the observer is given by the Doppler effect formula: $n_a = n \left( \frac{v}{v - v_s} \right

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$29.5 \, m/s, \, 200 \, Hz$

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(C) When the train is approaching,the frequency heard by the observer is given by the Doppler effect formula: $n_a = n \left( \frac{v}{v - v_s} ight)$.Substituting the values: $219 = n \left( \frac{340}{340 - v_s} ight)$ ... $(i)$.When the train is receding,the frequency heard by the observer is: $n_r = n \left( \frac{v}{v + v_s} ight)$.Substituting the values: $184 = n \left( \frac{340}{340 + v_s} ight)$ ... $(ii)$.Dividing equation $(i)$ by $(ii)$:$\frac{219}{184} = \frac{340 + v_s}{340 - v_s}$.$219(340 - v_s) = 184(340 + v_s)$.$74460 - 219v_s = 62560 + 184v_s$.$11900 = 403v_s$.$v_s \approx 29.53 \, m/s \approx 29.5 \, m/s$.Substituting $v_s$ back into equation $(i)$:$219 = n \left( \frac{340}{340 - 29.5} ight) = n \left( \frac{340}{310.5} ight)$.$n = \frac{219 	imes 310.5}{340} \approx 200 \, Hz$.

An observer standing at a station observes a frequency of $219 \, Hz$ when a train approaches and $184 \, Hz$ when the train goes away from him. If the velocity of sound in air is $340 \, m/s$,then the velocity of the train and the actual frequency of the whistle will be:

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