1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Calculating moving speaker through two detectors

  1. Jan 25, 2015 #1
    1. The problem statement, all variables and given/known data

    A speaker emitting sound at a frequency of 20 Hz is moving in the +x direction between two detectors. The speaker is moving at a speed of 30 m/s and the detectors are wired so that they flash red (λ = 700 nm) when the pressure is a maximum and green (λ = 700 nm) when the pressure is a minimum. Use 340 m/s as the speed of sound.

    [1] Calculate the distance between maxima ahead and behind the moving speaker.

    [2] Calculate the frequency of the light blinking on each of the detectors.

    [3] An observer between the detectors is moving at 0.8c in the +x direction. Calculate the frequencies for the red and green lights for each detector this observer sees.

    [4] Transform the velocity of the speaker to the observer frame as well as the velocity of sound in each direction.

    2. Relevant equations

    ##f' = f \frac{v \pm v_{receiver}}{v \pm v_{source}}##

    ##t' = \frac{t}{\sqrt{1-\frac{v^2}{c^2}}}##

    3. The attempt at a solution
    I am confused at the start with how the detectors detect maximum and minimum pressure and subsequently question1 about the maxima?
     
  2. jcsd
  3. Jan 25, 2015 #2

    Simon Bridge

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member
    2016 Award

    How the detectors work does not matter.
    Sound waves are pressure waves - the distance between two consecutive maxima of a wave has a special name.
     
  4. Jan 25, 2015 #3
    OK thanks, wavelength!

    [1] Calculate the distance between maxima ahead and behind the moving speaker.

    ##\lambda_{behind} = \frac{v_{sound} + v_{source}}{f} = 18.5 m##
    ##\lambda_{ahead} = \frac{v_{sound} - v_{source}}{f} = 15.5 m##

    [2] Calculate the frequency of the light blinking on each of the detectors.

    ##f = \frac{v}{\lambda} = 4.857 X 10^8 Hz##

    [3] An observer between the detectors is moving at 0.8c in the +x direction. Calculate the frequencies for the red and green lights for each detector this observer sees.

    ##T = \frac{v_{speaker} - v_{observer}}{1 - \frac{v_{speaker} v_{observer}}{c^2}} = 2.0588 X 10^{-9} s##

    ##T' = \frac{T}{\sqrt{1 - \frac{v^2}{c^2}}} = \frac{2.0588 X 10^{-9} s}{\sqrt{1 - \frac{(.8c)^2}{c^2}}} = 3.4314 X 10^{-9} s##

    ##f' = \frac{1}{T'} = 2.9143 X 10^8 s##

    [4] Transform the velocity of the speaker to the observer frame as well as the velocity of sound in each direction.

    ##v'_{speaker} = \frac{v_{speaker} - v_{observer}}{1 - \frac{v_{speaker} v_{observer}}{c^2}} = -2.3983486 X 10^8 m/s##

    ##v'_{sound +x direction} = \frac{v_{sound +x direction} - v_{observer}}{1 - \frac{v_{sound +x direction} v_{observer}}{c^2}} = \frac{340 m/s - .8c}{1 - \frac{(340 m/s)(.8c)}{c^2}} = -2.3985502 X 10^8 m/s##

    ##v'_{sound -x direction} = \frac{v_{sound +x direction} - v_{observer}}{1 - \frac{v_{sound +x direction} v_{observer}}{c^2}} = \frac{-340 m/s - .8c}{1 - \frac{(-340 m/s)(.8c)}{c^2}} = -2.39812182 X 10^8 m/s##

    What is throwing me off now is that the velocity of sound in the -x direction according to the observer's frame is moving slower than the sound moving in the +x direction. I would think that it should be the opposite?
     
  5. Jan 26, 2015 #4

    Simon Bridge

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member
    2016 Award

    In the observers reference frame, the detectors are moving in the -x direction at 0.8c ... one of the detectors is behind.
    You don't need the velocity of sound in the observer's frame to do the problem - only the frequency of the flashing lights in their rest frame and the relative velocities.
     
  6. Jan 26, 2015 #5
    Oh I see:

    ##v'_{ahead} = v_{ahead} - v_{observer} = \frac{f}{\lambda} - .8c = \frac{7X10^{-7}}{15.5} - .8c = -2.398335999999999548 X10^8 m/s##

    ##v'_{behind} = -v_{behind} - v_{observer} =- \frac{f}{\lambda} - .8c = -\frac{7X10^{-7}}{18.5} - .8c = -2.398336000000000378 X10^8 m/s##
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted



Similar Discussions: Calculating moving speaker through two detectors
  1. Two speakers (Replies: 0)

  2. Two Speakers Question (Replies: 5)

Loading...