Question
Two trains are traveling toward each other at 30.5 m/s relative to the ground. One train is blowinga whistle at 1060 Hz. (a) What frequency will be heard on the othertrain in still air?
1 Hz
(b) What frequency will be heard on the other train if the wind isblowing at 30.5 m/s toward the whistle andaway from the listener?
2 Hz
(c) What frequency will be heard if the wind direction isreversed?
3 Hz
Section 17-9 The Doppler Effect (a) What frequency will be heard on the othertrain in still air?
1 Hz
(b) What frequency will be heard on the other train if the wind isblowing at 30.5 m/s toward the whistle andaway from the listener?
2 Hz
(c) What frequency will be heard if the wind direction isreversed?
3 Hz
Section 17-9 The Doppler Effect
Explanation / Answer
Given frequency f = 1060Hz v = 343 m/s Two trains are traveling toward each other at 30.5 m/s relative to the ground a) the frequency heard in still air is f ' =f(v+vD/v-vS) =(1060Hz)(343+30.5/343-30.5) =---------Hz b) In a frame of reference where the air seems still , thevelocity of the detector is vD = 30.5 -30.5 = 0, andthat of the source is vS = 2(30.5) therefore f ' = f(v+vD/v-vS) =(1060Hz){343+0/343-2(30.5)} =---------Hz c) we again pick a frame of reference where the airseems still . Now , the velocity of the source is vS =30.5-30.5=0, and that of the detector is vD = 2(30.5) therefore f ' = f(v+vD/v-vS) =(1060Hz){343+2(30.5)/343-0} =---------Hz =(1060Hz){343+0/343-2(30.5)} =---------Hz c) we again pick a frame of reference where the airseems still . Now , the velocity of the source is vS =30.5-30.5=0, and that of the detector is vD = 2(30.5) therefore f ' = f(v+vD/v-vS) =(1060Hz){343+2(30.5)/343-0} =---------Hz =(1060Hz){343+2(30.5)/343-0} =---------Hz