A train sounds its whistle as it approaches and leaves arailroad crossing. An ob

Question

A train sounds its whistle as it approaches and leaves arailroad crossing. An observer at the crossing measures a frequencyof 219 Hz as the train approaches and a frequency of 184 Hz as thetrain leaves. The speed of sound is 340 m/s. Find the speed of thetrain and the frequency of the whistle. Thank you so much A train sounds its whistle as it approaches and leaves arailroad crossing. An observer at the crossing measures a frequencyof 219 Hz as the train approaches and a frequency of 184 Hz as thetrain leaves. The speed of sound is 340 m/s. Find the speed of thetrain and the frequency of the whistle. Thank you so much

Explanation / Answer

Speed of sound V = 340 m / s Speed of observer v = 0 Speed of train v ' = ? when train approaching to observer : ------------------------------------- f ' = [ V / (V -v ' ) ] f 219 = [ 340 / ( 340 - v ' ) ]f             f = [ ( 340 - v ' ) / 340 ] *219     ----( 1) when train leaves : ------------------ f " =   [ V / (V +v ' ) ] f 184 = [ 340 / ( 340 + v ' ) ]f             f = [ ( 340 + v ' ) / 340 ]* 184     ----( 2) from eq ( 1 ) and ( 2) , [ ( 340 - v ' ) / 340 ] * 219 = [ ( 340 + v ' ) /340 ] * 184 [ ( 340 + v ' ) / 340 ] = 1.1902 *[ (340 - v ' ) / 340 ]      340 + v ' = 404.67 - 1.1902 v ' 2.1902 v ' = 64.67             v ' = 29.52 m / s plug this value in eq ( 2 ) , f = [ ( 340 + 29.52 ) / 340 ] *184                                          =199.98 Hz                                         ~ 200 Hz    184 = [ 340 / ( 340 + v ' ) ]f             f = [ ( 340 + v ' ) / 340 ]* 184     ----( 2) from eq ( 1 ) and ( 2) , [ ( 340 - v ' ) / 340 ] * 219 = [ ( 340 + v ' ) /340 ] * 184 [ ( 340 + v ' ) / 340 ] = 1.1902 *[ (340 - v ' ) / 340 ]      340 + v ' = 404.67 - 1.1902 v ' 2.1902 v ' = 64.67             v ' = 29.52 m / s plug this value in eq ( 2 ) , f = [ ( 340 + 29.52 ) / 340 ] *184                                          =199.98 Hz                                         ~ 200 Hz

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