Doppler effect fire truck siren

[ryty]

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 460 Hz; as the truck recedes, you hear a tone of 420 Hz. How much time will it take for the truck to get from your position to the fire 5.0 km away, assuming it maintains a constant speed?
I can find the distance, but i need to know the velocity of the vehicle

Homework Equations

fo = fv/(v − vt)

The Attempt at a Solution

460=420/(343-v)
v=342 m/s
this isn't right

 

[Andrew Mason]

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 460 Hz; as the truck recedes, you hear a tone of 420 Hz. How much time will it take for the truck to get from your position to the fire 5.0 km away, assuming it maintains a constant speed?
I can find the distance, but i need to know the velocity of the vehicle

Homework Equations

fo = fv/(v − vt)

The Attempt at a Solution

460=420/(343-v)
v=342 m/s
this isn't right

Your doppler shift equation is not correct.

You have to use different doppler shift equations for approaching and receding sources:

For an approaching source:

$$f_{observed} = f_{actual}{\left(\frac{v_{sound}}{(v_{sound} - v_{source})}\right)$$

For a receding source:

$$f_{observed} = f_{actual}{\left(\frac{v_{sound}}{(v_{sound} + v_{source})}\right)$$

You know that the actual frequency in each case is the same, and the firetruck speed is the same.

You also know that the magnitude of the wavelength shift will be the same (this is because the difference in wavelength between the actual and observed sound is the distance the truck moves in the period of one vibration). For the approaching truck the wavelength shift is negative and for the receding truck the shift is positive . You can determine the actual frequency from that wavelength shift.

Work out the speed of the truck from that. Then work out the time for the truck to go 5 km.

AM