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 crossinghear? 2. A crow is flying above the railroad track towards the trainand hears a frequency of 685Hz. How fast, and in what direction isit moving with respect to the train? 3. A passerger on the train sprints towards from the enginetowards the end of the train at constant rate of 10m/s. Whatfrequency does he hear? 4. Treat the whistle as a hemispherical emitter and calculatethe source power if the whistle can just be heard at a distance of20Km ahead of the train. The threshold of hearing is at a soundintensity of 10-8W/m2. I promise to rate you aslifesavers if 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 crossinghear? 2. A crow is flying above the railroad track towards the trainand hears a frequency of 685Hz. How fast, and in what direction isit moving with respect to the train? 3. A passerger on the train sprints towards from the enginetowards the end of the train at constant rate of 10m/s. Whatfrequency does he hear? 4. Treat the whistle as a hemispherical emitter and calculatethe source power if the whistle can just be heard at a distance of20Km ahead of the train. The threshold of hearing is at a soundintensity of 10-8W/m2. I promise to rate you aslifesavers if your answer is correct!

Explanation / Answer

In classical physics (waves in a medium), the relationshipbetween observed frequency f and emitted frequencyf0 is given by f = (v + vr/v + vs) * fo f is the observed frequency f is the observed frequency v is the velocity of sound waves vr is the velocity of the receiver vs is the velocity of the source fo is the emitted frequency 1.the frequency heared by a farmer stopped at the crossingis f = (v + vr/v + vs) * fo--------------(1) here,v = 340 m/s vr = 0 vs= -144 km/h = -144 * (1000/3600) m/s = -40m/s fo= 600 Hz 2.the frequency heared by the crow is f = 685 Hz let the speed of the crow be vr solving equation (1) for vr we get vr= v * {(f/fo) - 1} + (f/fo)* vs f = 685 Hz,fo= 600 Hz and vs= -40m/s (3)the frequency heared by the passenger is f = (v + vr/v + vs) *fo vr= 10 m/s,vs= 40 m/s and fo=600 Hz (4)We define the intensity I of a wave,or the power per unitarea,as the rate at which the energy transported by the wavetransfers through a unit area A perpendicular to the direction oftravel of the wave: I = (P/A) = (P/2r^2) or P = I * 2r^2 I = 10 ^-8 W/m^2 and r = 20 km = 20 * 10^3 m f = 685 Hz,fo= 600 Hz and vs= -40m/s (3)the frequency heared by the passenger is f = (v + vr/v + vs) *fo vr= 10 m/s,vs= 40 m/s and fo=600 Hz (4)We define the intensity I of a wave,or the power per unitarea,as the rate at which the energy transported by the wavetransfers through a unit area A perpendicular to the direction oftravel of the wave: I = (P/A) = (P/2r^2) or P = I * 2r^2 I = 10 ^-8 W/m^2 and r = 20 km = 20 * 10^3 m

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