Quantcast

Got Homework?

Connect with other students for help. It's a free community.

  • across
    MIT Grad Student
    Online now
  • laura*
    Helped 1,000 students
    Online now
  • Hero
    College Math Guru
    Online now

Here's the question you clicked on:

55 members online
  • 0 replying
  • 0 viewing

modphysnoob Group Title

A spacecraft traveling out of the solar system at 0.92c sends back information at a rate of 400Hz. At what rate do we receive the information?

  • one year ago
  • one year ago

  • This Question is Closed
  1. modphysnoob Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    @Jemurray3

    • one year ago
  2. Jello_Submarine Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    According to my calculations - at the rate of 400 Hz, because after adding up speed of the radio waves(c) and speed of the spacecraft(0,92) regarding the theory of special relativity, the answer is c and therefore the rate stays the same because the speed of the radiowaves is same.

    • one year ago
  3. Jello_Submarine Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    0.92c should be behind the word "spacecraft"

    • one year ago
  4. modphysnoob Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    I was given following options A. 1960Hz B. 17Hz C. 9600Hz D. 82Hz.

    • one year ago
  5. Jello_Submarine Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    oh...let me rethink

    • one year ago
  6. Jello_Submarine Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    definitely not 1960 Hz nor 9600 Hz, because as the speed increases, the waves are further apart therefore frequency received has to be lower than frequency transmitted.

    • one year ago
  7. Jello_Submarine Group Title
    Best Response
    You've already chosen the best response.
    Medals 1

    hmm, whatever I do, it still adds up to c. \[\lambda = 750000m\] if it helps

    • one year ago
  8. modphysnoob Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    I appreciate any help

    • one year ago
  9. Jemurray3 Group Title
    Best Response
    You've already chosen the best response.
    Medals 2

    This is a Doppler shift problem. Just to make sure you have the idea right, we'll derive the equation here. Question: At what frequency does the spaceship see the observer receiving information? The distance between crests in the ship frame is simply the wavelength lambda. However, in the time it takes for the light to travel one wavelength, the earth will have moved. The time between crests is therefore: \[ t = \frac{\lambda + vt}{c} \implies ct = \lambda + vt \implies t = \frac{\lambda}{c-v} \] Since we are talking about electromagnetic radiation, lambda = c / frequency, so \[ t = \frac{c}{c-v} \frac{1}{f} = \frac{1}{1-v/c} \frac{1}{f} \] Now what about the observer? The proper time for the reception of information is calculated in the observer's frame, because the receiver is stationary there. Therefore, the observer measures this time to be \[t' = t/\gamma = \frac{\sqrt{1-v^2/c^2}}{1 - v/c} \frac{1}{f} = \sqrt{\frac{1+v/c}{1-v/c} } \frac{1}{f} \] Therefore, the frequency measured by the observer will be \[ f_o = \sqrt{\frac{1-\beta}{1+\beta} } f_s\] where \[f_0, f_s, \beta \] are the observer frequency, the source frequency, and v/c respectively. Plugging numbers in, that gives me ~82 Hz, a redshift, as expected.

    • one year ago
  10. modphysnoob Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    thanks you man, I will read it and ask if anything is unclear

    • one year ago
  11. modphysnoob Group Title
    Best Response
    You've already chosen the best response.
    Medals 0

    where did the beta come from?

    • one year ago
  12. Jemurray3 Group Title
    Best Response
    You've already chosen the best response.
    Medals 2

    beta = v/c is just a shorthand that we use

    • one year ago
    • Attachments:

See more questions >>>

Your question is ready. Sign up for free to start getting answers.

spraguer (Moderator)
5 → View Detailed Profile

is replying to Can someone tell me what button the professor is hitting...

23

  • Teamwork 19 Teammate
  • Problem Solving 19 Hero
  • You have blocked this person.
  • ✔ You're a fan Checking fan status...

Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.

This is the testimonial you wrote.
You haven't written a testimonial for Owlfred.