Solve Doppler Problems: Train & Person

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To solve the Doppler effect problem involving a train and a stationary observer, the relevant formula is f' = f (v + vo) / (v - vs), where f' is the observed frequency, f is the source frequency, v is the speed of sound, vo is the observer's speed, and vs is the source speed. The train approaches at 35.0 m/s while emitting a whistle at 2.5 kHz. When calculating the frequency heard by the observer as the train approaches, the source speed should be treated as negative to account for the increase in frequency. As the train recedes, the source speed becomes positive, resulting in a lower observed frequency. Understanding the correct application of the formula is crucial for accurate results in Doppler problems.
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Homework Statement


A train approaches an observer at 35.0 m/s and passes a person stading on the side of the track. The whistile is sounding at 2.5 kHz. What frequency will the person hear as the train approaches? When it recedes?

Homework Equations


f' = f \frac{v \pm v<sub>o</sub>}{v \mp v<sub>s</sub>}

The Attempt at a Solution


f' = 2500 Hz(?)

I don't know what number I should put into the equation.
 
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Yes, what a miserable formula that is!
It looks a little better here: http://en.wikipedia.org/wiki/Dopplar_Effect
(scroll down 1 screenfull)
Since the receiver is not moving, the formula is
f = fi*V/(V + Vs)
Here V is the speed of sound in air, and Vs is the speed of the source. The speed of the source toward the receiver increases the frequency, so you must make Vs a negative number (dividing by a smaller number makes the result larger).
 
Thread 'Variable mass system : water sprayed into a moving container'

Thread 'Variable mass system : water sprayed into a moving container'

Starting with the mass considerations #m(t)# is mass of water #M_{c}# mass of container and #M(t)# mass of total system $$M(t) = M_{C} + m(t)$$ $$\Rightarrow \frac{dM(t)}{dt} = \frac{dm(t)}{dt}$$ $$P_i = Mv + u \, dm$$ $$P_f = (M + dm)(v + dv)$$ $$\Delta P = M \, dv + (v - u) \, dm$$ $$F = \frac{dP}{dt} = M \frac{dv}{dt} + (v - u) \frac{dm}{dt}$$ $$F = u \frac{dm}{dt} = \rho A u^2$$ from conservation of momentum , the cannon recoils with the same force which it applies. $$\quad \frac{dm}{dt}...
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