# Speed of a jet (challenging doppler effect)

• Ethan_Tab
In summary, at an air show, a fighter jet flying at half the speed of sound is observed to have a frequency drop by one octave as it approaches and directly passes overhead. Using the equation ƒobs=ƒo(v+-d/v+-s), where ƒo is the original frequency, d is the velocity of the detector, s is the velocity of the source, and v is the velocity of sound, the speed of the jet can be calculated as mach 0.5. However, it is important to note that there may be more variables than equations, so caution should be taken when interpreting the result.
Ethan_Tab

## Homework Statement

At an air show, a fighter jet does manuevers past the crowd. Your increible hearing notes that the frequnecy of the sound coming from the jet engine drops exactly by one octave when it is approaching you to when it is directly above you (not moving relitive to you). How fast is the jet flying?

## Homework Equations

Mach #= velocity/velocity sound
ƒobs=ƒo(v+-d/v+-s) where ƒo= frequency original, d= velocity of detector, s= velocity of source and v is the velocity of sound.

## The Attempt at a Solution

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Since a drop by one octave is the same as half the frequency, we can represent the frequency observed when the plane approaches as ƒ and the frequency heard directly above as f/2.

we can then make two equations;
Approaching--- ƒ=ƒo(v/v-s)
Directly above--- ƒ/2=ƒo(v/v) (no s since its not moving relative to you at that exact moment)

However there are still more variables then equation, not sure how to go on from here.

Hello ET,

Scary story! jet plane overhead, not moving relative to you. Hanging from a thread ? With engine running ?

Never mind. Your notation is awful, but in ##f/2 = f_0## I see one variable disappearing, so you are left with one frequency only. Write out the equation and have a eureka moment !

Ethan_Tab
Eureka indeed.

I got the answer as being mach 0.5 for the speed of the plane. Would you concur?

The picture of a jet plane coming straight at you at half the speed of sound is also rather terrifying! Better step aside real fast !

And your answer is exactly what I got -- so either we're both right or both wrong

Ethan_Tab

## 1. What is the Doppler effect and how does it affect the speed of a jet?

The Doppler effect is the change in frequency or wavelength of a wave as it moves towards or away from an observer. In the case of a jet, the Doppler effect can make it appear to be moving faster or slower depending on the direction it is traveling in relation to the observer.

## 2. How does the Doppler effect make it challenging to accurately measure the speed of a jet?

The Doppler effect can make it challenging to accurately measure the speed of a jet because it can alter the perceived frequency of sound waves emitted by the jet. This can lead to errors in calculating the actual speed of the jet.

## 3. What factors can affect the speed of a jet and complicate the use of the Doppler effect?

Factors such as wind speed, air temperature, and altitude can affect the speed of a jet and complicate the use of the Doppler effect. These factors can alter the speed of sound, which is a key component in calculating the speed of a jet using the Doppler effect.

## 4. How can scientists account for these factors when using the Doppler effect to measure the speed of a jet?

Scientists can use weather data and other atmospheric conditions to make adjustments and account for the factors that may affect the speed of sound. They can also use advanced technologies and algorithms to accurately calculate the speed of a jet despite these complicating factors.

## 5. What are some other methods scientists can use to measure the speed of a jet besides the Doppler effect?

Scientists can also use radar, GPS tracking, and onboard instruments such as airspeed indicators to measure the speed of a jet. These methods are not affected by the Doppler effect and can provide more accurate readings of the jet's speed.

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