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Answer to Question #2719 in Mechanics | Relativity for ABHYUDAY

Question #2719
TRAIN A IS MOVING WITH SPEED 1OOkm/hr & train b moving with speed 150 km/hr.train b whistles at 800Hz.In how much time a passenger sitting in train A will hear it?
Expert's answer
Train A is moving with speed 100 km/h and train B with speed 150 km/h. Train B whistles at 800 Hz. In how much time a passenger sitting in train A will hear it?
Let’s start. The general Formula is
ν= ν0 (s±V)/(s±v),
where: s - is the velocity of waves in the medium, V - is the velocity of the receiver (passenger in train A) relative to the medium; positive if the receiver is moving towards the source, v - is the velocity of the source (train B) relative to the medium; positive if the source is moving away from the receiver.
The initial frequency is 800 [Hz], so we get
ν= ν0 (s±V)/(s±v)= ν0 (s+V)/(s-v).
V=100 [km/h] = (100*1000[m])/(3600[sec])=27.7 [m/sec], v=150 [km/h] =41.6 [m/sec].
In dry air at 20 °C (68 °F), the speed of sound is 343.2 metres per second, so we get
ν= ν0 (s+V)/(s-v)= ν0 (s+V)/(s-v)=800[Hz] (343.2+27.7)/(343.2-41.6)=800[Hz]*370.9/301.6=800[Hz]*1.23=983.8[Hz].
If the trains are moving toward each other in other case
ν= ν0 (s+V)/(s+v)= ν0 (s+V)/(s+v)=800[Hz] (343.2+27.7)/(343.2+41.6)=800[Hz]*370.9/384.8=800[Hz]*0.96=773.1[Hz].

So the answer is ν=(983.8 Hz, 773.1Hz).

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