What is the solution to the Doppler Effect and Fire Truck Homework?

[MaluDude]

Homework Statement

Hearing the siren of an approaching fire truck, you pull over to the side of the road and stop. As the truck approaches, you hear a tone of 470 Hz; as the truck recedes, you hear a tone of 400 Hz. How much time will it take the truck to get to the fire 2.5 km away assuming it maintain a constant speed?

Homework Equations

f'=f(v/(v+(or minus) v_s))
y_f=y_i+v_it+1/2at²

The Attempt at a Solution

I tried to plug in 470 and 400 for f', but I did not know what to do after that.

 

[LongLiveYorke]

Your first relevant equation relates the true frequency f to the doppler shifted frequency f' that results from the object moving toward or away from you at a speed v. To find the time it takes for the truck to travel, we're going to have to calculate its velocity v.

I would first think about the situation presented in the problem and how to apply your first relevant equations. Be sure to first understand the meaning of the variables in that equation. If f in the equation is the stationary frequency of the noise, do we want to plug either 400 or 470 into f?

 

[lanedance]

so there are 2 separate doppler effects here - one when the truck is appraoching, one when it is receding

so you need to solve for 2 unknowns, true fs (source frequency) and the velocity

 

[MaluDude]

Why would you want to put those 2 values into your stationary f value? Wouldn't you want to include those values for the changed f-values? Also couldn't you say that the speed of sound is just 334?

 

[lanedance]

you have to ask yourself what you are trying to find... the truck velocity

unknowns:
source frequency (somewhere between 400 & 470) and source velocity (ie truck speed)
knowns:
spped of sound

you know the doppler changed frequencies for the approaching truck & receding

you should be able to write a doppler equation with the 2 unknowns in each case, and solve for the truck velocity...