A train is traveling at 144km/h. As it approaches a railroadcrossing the whistle

Question

A train is traveling at 144km/h. As it approaches a railroadcrossing the whistle on the front of the train emits a 600Hztone. 1. What frequency does a farmer stopped at the crossing hear? 2. A crow is flying above the railroad track towards the train andhears a frequency of 685Hz. How fast, and in what direction is itmoving with respect to the train? 3. A passerger on the train sprints towards from the engine towardsthe end of the train at constant rate of 10m/s. What frequency doeshe hear? 4. Treat the whistle as a hemispherical emitter and calculate thesource power if the whistle can just be heard at a distance of 20Kmahead of the train. The threshold of hearing is at a soundintensity of 10-8W/m2.
Please show all your work, and I promise to rate you as lifesaversif your answer is correct! A train is traveling at 144km/h. As it approaches a railroadcrossing the whistle on the front of the train emits a 600Hztone. 1. What frequency does a farmer stopped at the crossing hear? 2. A crow is flying above the railroad track towards the train andhears a frequency of 685Hz. How fast, and in what direction is itmoving with respect to the train? 3. A passerger on the train sprints towards from the engine towardsthe end of the train at constant rate of 10m/s. What frequency doeshe hear? 4. Treat the whistle as a hemispherical emitter and calculate thesource power if the whistle can just be heard at a distance of 20Kmahead of the train. The threshold of hearing is at a soundintensity of 10-8W/m2.
Please show all your work, and I promise to rate you as lifesaversif your answer is correct!

Explanation / Answer

the speed of the train is vs= 144 km/h = 144 *(1000/3600) m/s = 40 m/s the frequency emitted by the whistle is fo= 600Hz 1.the frequency heared by the farmer is f = (v + vr/v + vs) * fo------------(1) v = 340 m/s,vr= 0 and vs= -40 m/s 2.the frequency heared by the crow is f = 685 Hz solving equation (1) for vr we get vr = v * ((f/fo) - 1) + vs*(f/fo) 3.the frequency heared by the passenger is f = (v + vr/v + vs) *fo vr = -10 m/s and vs= 40 m/s 4.the source power is P = I * A = I * 2r^2 I = 10^-8 W/m^2 and r = 20 km = 20 * 10^3 m v = 340 m/s,vr= 0 and vs= -40 m/s 2.the frequency heared by the crow is f = 685 Hz solving equation (1) for vr we get vr = v * ((f/fo) - 1) + vs*(f/fo) 3.the frequency heared by the passenger is f = (v + vr/v + vs) *fo vr = -10 m/s and vs= 40 m/s 4.the source power is P = I * A = I * 2r^2 I = 10^-8 W/m^2 and r = 20 km = 20 * 10^3 m

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