Frequency of Horn: Solving Doppler Equation

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The discussion revolves around solving a Doppler effect problem involving two trains. The first part correctly calculates the frequency detected by a stationary train as 322.7 Hz when a train moving away at 29 m/s blows a 350 Hz horn. In the second part, the user initially calculates the detected frequency for a second train moving away at 15.6 m/s as 334.77 Hz but realizes that they need to consider the relative velocity of both trains. By adding the speeds of both trains, they derive a new frequency of 309.72 Hz, seeking confirmation on this calculation. The user is looking for validation of their logic and whether this final answer is correct.
European Sens
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There are two questions here:

1st is...

The velocity of sound in air is 343 m/s. A train moving away from a detector at 29 m/s blows a 350 Hz horn. What frequency is detected by a stationary train?

I got the correct answer of 322.7 using dopplers equation.

Now part 2 is...

What frequency is detected by a train moving away from the first train at a speed of 15.6 m/s?

Plugging in ---->

f' = [350*343] / [343+15.6] = 334.77

It seems correct to me, but when I submitted my answer online I was incorrect.

Please help! Thanks!
 
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Try and imagine how fast train number two is moving away from train number one i.e. work out train number one's velocity relative to train number two and use that in the equation.
 
well train # 1 is going 29 m/s and train # 2 is going 15.6 m/s in opposite directions... that I know.

So do I add 29 + 15.6 to get 44.6 m/s away from each other...

which when plugged in is:
f' = [350*343] / [343+44.6] = 309.72


Please advice. Thank you.
 
Does my logic seem correct. Please lead me in the right direction. Thanks once again.
 
Yes that looks right, is it not the right answer?
 
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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