What is the distance traveled by a rollercoaster based on the Doppler effect?

In summary, the problem involves estimating the distance a rollercoaster moves as it comes to a stop, based on the change in pitch of the sound of riders' screams. Using the given equation and information, students can solve for the velocity of the rollercoaster and then use it to calculate the distance traveled.
  • #1
starhallie
16
0

Homework Statement



Standing in line next to the scariest rollercoaster of all time, you see your friends screaming their heads off as they come speeding out of the end of the ride. The sound of their screams is about 30% higher in pitch than normal due to the Doppler shift caused by their motion towards you. If they sound normal again by the time the rollercoaster has halted about 1.5 seconds later, estimate how far the rollercoaster moved as it was coming to rest.

Homework Equations



f(observed)= f(emitted)((v(sound) +/- v(observer)/(v(sound) +/- v(source))

The Attempt at a Solution



My hunch on this problem is that I need to create some sort of ratio with the 30% given in the problem in order to solve it, and I know I'll have to do some algebra to get a velocity for my final answer. Would anyone be willing to brainstorm this with me? I'd really appreciate it!
 
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  • #2
starhallie said:

Homework Equations



f(observed)= f(emitted)((v(sound) +/- v(observer)/(v(sound) +/- v(source))

Yes, you'll need to use this equation to find v(source). Some other information to use:

What is v(observer)?
What's another relation between f(observed) and f(emitted), using the information given in the problem statement?
 
  • #3
Thank you for the help. I ended up figuring it out!
 

FAQ: What is the distance traveled by a rollercoaster based on the Doppler effect?

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 wave source. This phenomenon is commonly observed with sound waves, such as the change in pitch of a siren as an ambulance passes by.

How does the Doppler effect work?

The Doppler effect occurs because the motion of the observer causes the wave source to have a different relative velocity, resulting in a change in the perceived frequency or wavelength. This can be understood in terms of the compression and expansion of the wave as the observer moves towards or away from the source.

What is the formula for calculating the Doppler effect?

The formula for calculating the Doppler effect is:
fobs = fsource x (v±vobs) / (v±vsource)
where fobs is the observed frequency, fsource is the source frequency, v is the speed of the wave, vobs is the observer's speed, and vsource is the source's speed.

What are some real-life applications of the Doppler effect?

The Doppler effect has many practical applications, including radar technology, weather forecasting, and medical imaging. It is also used in astronomy to determine the relative motion of celestial bodies and in the study of the expansion of the universe.

How is the Doppler effect related to the redshift and blueshift of light?

The Doppler effect is responsible for the redshift and blueshift of light, which is the shift in the wavelength of light due to the relative motion between the light source and the observer. When the source is moving away, the light appears redshifted, and when the source is moving towards, the light appears blueshifted. This phenomenon is crucial in understanding the expansion of the universe and the study of distant galaxies.

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