# Doppler effect, offset from line of effect

• cheff3r
In summary, a man records the frequency of an ambulance's siren at 5100Hz while it is 20m away and traveling at a speed of 20 m/s. The frequency recorded when the ambulance is approaching the man is 5415Hz and when it is moving away it is 4819Hz. To find the frequency when the man is off the road, the cos angle can be used to find the equivalent velocity along the direction from the man to the ambulance.
cheff3r
sorry lots of reading but i wanted to explain what I've done (tried to do)

## Homework Statement

An ambulance has a loud siren, which emits a pure note at 5100Hz. A man 20 m from a straight road along which the ambulance is travelling, and records the frequency of the sound he hears from the siren. There is no wind. When the ambulance is approaching the man and a long way from the man what frequency is recorded? what frequency is heard after the ambulance pass the observer and recedes into the distance? the ambulance speed is 20 m/s.

Bonus marks if you find the frequency by the man at t=-1s and t=2s where t=0 is when the ambulance is closest to the man

## Homework Equations

Speed of sound 343 m/s
f'= $$\frac{v}{v-v(s)}$$ f

## The Attempt at a Solution

So far off into each distance is just straight forward Doppler effect
f'= $$\frac{v}{v-v(s)}$$ f

getting when traveling towards the man f'=5415Hz which seems correct since its traveling towards the detector yes?
and when traveling away from man f'=4819Hz which also seems to be correct since its traveling away the detectors yes?

here's when I get into a bit of trouble if he is off the road (I'm taking it as he is on a side road perpendicular to the main road) I have found two sources saying take the cos angle and one saying take sin angle (so I going to use cos angle for now, but is this right?) and I'm not sure how to multiply it into the equation this is what I tried,

this was a guess am I doing it right of do I do it a different way (my main problem)
f'= $$\frac{v}{v-sin (\theta)v(s)}$$ f

after I get the equation right would I have to do a couple triangles to find the angle created when the ambulance is 20 meters away (1 second) and 40 meters away (2 seconds)

The only difference, when the ambulance is close, is that it's not coming directly at him. Just find the speed along the direction from him to the ambulance, and plug that into your equation and you're good.

Ahh good idea, so your saying find the an equivalent velocity (or proportion) of the ambulance in the direction straight towards the observer that makes sense.
thanks

## 1. What is the Doppler effect?

The Doppler effect is a phenomenon that occurs when there is a relative motion between a source of waves and an observer. It causes a perceived change in frequency of the waves, which is dependent on the direction and speed of the motion.

## 2. How does the Doppler effect apply to sound waves?

In the case of sound waves, the Doppler effect causes a perceived change in pitch when there is a relative motion between the source of the sound and the listener. For example, when an ambulance with its siren on is moving towards you, the pitch of the siren will sound higher than when it is stationary or moving away from you.

## 3. What is meant by "offset from line of effect" in the Doppler effect?

The "line of effect" refers to an imaginary line that connects the source of the waves and the observer. The "offset" refers to the displacement of the source from this line. This offset can affect the perceived change in frequency of the waves, and is important to consider in certain scenarios, such as when the source is moving at an angle to the observer.

## 4. How is the Doppler effect used in astronomy?

In astronomy, the Doppler effect is used to study the motion and properties of celestial objects. By measuring the frequency shift of light emitted from a celestial object, scientists can determine its velocity and direction of motion. This technique has been used to discover exoplanets, study the expansion of the universe, and more.

## 5. Can the Doppler effect be observed in everyday life?

Yes, the Doppler effect can be observed in many everyday situations, such as when a car drives by with its horn honking, or when a train passes by with its whistle blowing. It is also commonly used in speed detection devices, such as radar guns used by law enforcement.

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