1)An alert physics student stands beside the tracks as a train rolls slowly past

Question

1)An alert physics student stands beside the tracks as a train rolls slowly past. He notes that the frequency of the train whistle is 461 Hz when the train is approaching him and 442 Hz when the train is receding from him. Using these frequencies, he calculates the speed of the train. What value does he find? (Assume the speed of sound in air is 343 m/s.)

2)In the arrangement shown in the figure below, an object of mass m = 4.0 kg hangs from a cord around a light pulley. The length of the cord between point P and the pulley is L = 2.0 m. (Ignore the mass of the vertical section of the cord.)

(a) When the vibrator is set to a frequency of 160 Hz, a standing wave with six loops is formed. What must be the linear mass density of the cord?

(b) How many loops (if any) will result if m is changed to 9.00 kg? (Enter 0 if no loops form.)
loops

(c) How many loops (if any) will result if m is changed to 10 kg? (Enter 0 if no loops form.)
loops

Explanation / Answer

While the train was coming towards the student

f * v / (c - v) = 461 ---------------------------(1)

While the train was receding away

f * v / (c + v) = 442 ----------------------------(2)

divide the both equations (1) and (2)

(c + v) / (c - v) = 461 / 442

442 c + 442 v = 461 c - 461 v

442 v + 461 v = 461 c - 442 c

903 v = 19 * 343

v = 7.22 m/s

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