# Doppler effect fire truck siren

• ryty
In summary: OUNT OF TIMEIn summary, the problem involves determining the amount of time it will take for an approaching fire truck to travel 5.0 km to a fire while maintaining a constant speed, based on the change in frequency of its siren as it approaches and recedes. To solve this, you need to use different Doppler shift equations for approaching and receding sources and consider the magnitude of the wavelength shift, which will be the same for both cases. From there, you can determine the speed of the truck and then calculate the amount of time it will take for it to reach the fire.
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

fo = fv/(v − vt)

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

ryty said:

## 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

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

Last edited:
.

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.

## 1. What is the Doppler effect?

The Doppler effect is the change in frequency or wavelength of a wave in relation to an observer who is moving relative to the source of the wave. This effect is commonly observed in sound waves, such as the sound of a fire truck siren.

## 2. How does the Doppler effect apply to a fire truck siren?

As a fire truck approaches, the sound waves from its siren are compressed, resulting in a higher frequency and a higher pitch. As the fire truck moves away, the sound waves are stretched, resulting in a lower frequency and a lower pitch. This change in frequency is known as the Doppler effect.

## 3. Why is the Doppler effect important for fire trucks?

The Doppler effect allows us to determine the direction and speed of a moving object, such as a fire truck. By listening to the change in pitch of the siren, we can tell if the fire truck is getting closer or farther away, and how fast it is moving.

## 4. Does the Doppler effect only apply to sound waves?

No, the Doppler effect can also be observed in other types of waves, such as light waves. For example, when a star is moving away from us, its light waves are stretched, resulting in a shift towards the red end of the spectrum, known as redshift. This is a key concept in the study of the universe and the Big Bang theory.

## 5. Can the Doppler effect be used for anything besides determining the speed of a moving object?

Yes, the Doppler effect has many practical applications, such as in weather radar and medical imaging. It is also utilized in everyday devices such as speed guns and radar detectors. Additionally, the Doppler effect has been studied extensively in fields such as physics and astronomy, leading to a better understanding of the universe.

Replies
1
Views
4K
Replies
6
Views
6K
Replies
4
Views
1K
Replies
3
Views
2K
Replies
1
Views
10K
Replies
3
Views
2K
Replies
4
Views
4K
Replies
9
Views
7K
Replies
22
Views
5K
Replies
4
Views
2K