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

 

[kerimek]

.



The Doppler effect refers to the change in frequency of a sound wave as the source moves closer or farther away from the observer. In this case, the approaching fire truck is the source of the sound, and as it moves towards you, the frequency of the siren appears higher, and as it moves away, the frequency appears lower. This phenomenon is described by the equation fo = fv/(v-vt), where fo is the observed frequency, fv is the frequency of the source, v is the speed of sound, and vt is the velocity of the source.

To calculate the time it takes for the truck to travel 5.0 km, we need to know the velocity of the truck. Without this information, we cannot accurately determine the time. However, we can use the given information to calculate the velocity of the truck.

From the given information, we know that the difference in frequencies is 40 Hz (460 Hz - 420 Hz) and the speed of sound is approximately 343 m/s. Using the equation for the Doppler effect, we can set up the following equation:

40 Hz = 460 Hz/(343 m/s - vt)

Solving for vt, we get a velocity of approximately 339 m/s. This is the velocity of the truck towards you. To find the total velocity of the truck, we need to add the velocity of sound (343 m/s) to this value, giving us a total velocity of 682 m/s.

Now, to calculate the time it takes for the truck to travel 5.0 km, we can use the equation v = d/t, where v is the velocity, d is the distance, and t is the time. Rearranging this equation, we get t = d/v. Plugging in the values, we get t = 5.0 km / 682 m/s = 7.34 seconds. Therefore, it would take approximately 7.34 seconds for the truck to travel 5.0 km at a constant speed of 682 m/s.