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Doppler Effect/Projectile Motion

  1. May 26, 2014 #1
    1. The problem statement, all variables and given/known data

    Find the frequency heard as you walk away from a building that has a fire alarm going off with a frequency of 2650 Hz. The velocity of the alarm is equivalent to the final velocity of an object being launched with an initial velocity of 235.4 km/h [W23°N] from a height of 5321 m. Assume air temperature to be -8.63°C.

    This was a very confusing question on a recent assignment. This is exactly how it is worded.

    The underlined parts make no sense to me,
    "You walk away from a building" this would mean that vobs has a value greater than 0, but this value is not given therefore I think the question is impossible.
    "The velocity of the alarm" This makes no sense since the alarm should be fixed to the building. I assumed it to have a velocity anyways in my solution.

    2. Relevant equations

    Doppler Effect Equation:
    fobs = frequency detected by the observer
    f0 = Actual frequency
    vs = speed of sound
    vobs = velocity of the observer
    vsou = velocity of the source

    fobs = (vs+vobs/vs+vsou)f0

    For the projectile motion part

    Trigonometric ratios to find the vertical and horizontal components of initial velocity.

    v22 = v12 + 2aΔd

    Pythagorean theorem to find final velocity using vertical and horizontal components.

    3. The attempt at a solution

    Projectile motion part

    Givens:
    v1 = 235.4 km/h = 65.39 m/s [W23°N]
    θ = 23°
    dy = 5321 m
    ay = 9.8 m/s2

    Solution:
    -Find vertical and horizontal component of initial velocity:

    sinθv1 = v1y
    25.55 m/s = v1y

    cosθv1 = vx
    60.19 m/s = vx

    velocity on the x-axis is assumed to be constant.

    -Find vertical component of final velocity:

    v2y2 = v1y2 + 2ad
    v2y = 323.95 m/s

    -Find final velocity

    v22 = v2y2 + vx2
    v2 = 329.49 m/s



    Doppler Effect Part

    Givens:
    f0 = 2650 Hz
    T = -8.63°C
    vsou = 329.49 m/s

    -Find the speed of sound

    vs = 331.4 + (0.606)(-8.63)
    vs = 326.17 m/s

    -Find the frequency heard by the observer

    fobs = (vs + vobs/vs + vsou)f0

    Missing vobs. Is the question impossible?
    1. The problem statement, all variables and given/known data



    2. Relevant equations



    3. The attempt at a solution
     
  2. jcsd
  3. May 9, 2015 #2
    By the velocity of the alarm they mean the velocity of the alarm with respec to you at a stand still. This is just a change of reference, it is the same as saying the velocity of you with respect to the alarm, or your speed if the alarm stood still (all be it in the oposite direction). i.e. speed of the alarm would then be the speed source-speed of the observer.
     
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