1. Not finding help here? Sign up for a free 30min 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!

Police car siren (waves)

  1. Feb 23, 2008 #1

    ~christina~

    User Avatar
    Gold Member

    [SOLVED] police car siren (waves)

    1. The problem statement, all variables and given/known data
    A police car speeds toward a warehouse door with its siren emitting sinusoidal waves of frequency fs = 300 Hz, intending to crash through the door. The car moves at 30 m / s and the ambient temperature is 35º C.

    (a) What is the wavelength of the wave if the siren is stationary?

    (b) Find the wavelengths of the waves in front of and behind the source when the siren is moving at 30 m / s.

    (c) What frequency does the driver of the police car hear reflected from the warehouse?

    (d) Does the driver detect a beat frequency? If yes, then find the beat frequency; if no, explain why not.

    2. Relevant equations
    [tex]v= (331m/s) \sqrt{1 + Tc/ 273} [/tex]

    [tex] \lambda = v/f [/tex]

    [tex] \lambda' = \lambda \pm vs/f [/tex]

    [tex] f '= (v/(v-vs))f [/tex]

    3. The attempt at a solution

    a) wavelength if the siren is stationary

    temp = [tex] 35 ^oC [/tex]
    f= 300Hz

    [tex]v= (331m/s) \sqrt{1 + Tc/ 273} [/tex]

    [tex]v= (331m/s) \sqrt{1 + 35 ^oC [/tex]/ [tex] 273 ^oC [/tex]

    v= 351.578m/s

    [tex] \lambda = v/f [/tex]
    [tex] \lambda[/tex] = 351.578m/s / 300Hz = 1.172m

    b) find the wavelengths of the waves in front of and behind the source if the siren is moving at 30m/s

    Not sure if this is the right equation for what they are asking but I used it for both in front of and behind the source wavelengths => [tex] \lambda' = \lambda \pm vs/f [/tex]

    ALSO NOT SURE IF LAMBDA (without ') is the wavelength I found in part a) but I used it....could be incorrect but I don't see where I'd get lambda if I didn't use that one for lambda in equation.

    front of car wavelength:
    [tex] \lambda'_{front} = \lambda \pm vs/f [/tex]

    [tex] \lambda'_{front} = 1.172m - (30m/s)/ 300Hz = 1.072m[/tex]

    back of car wavelength:

    [tex] \lambda'_{back} = \lambda \pm vs/f [/tex]

    [tex] \lambda'_{back} = 1.172m + (30m/s)/ 300Hz = 1.272m [/tex]

    c) frequency that the driver of the police car hears reflected from the wareheouse
    I looked it up and I think that the frequency of the reflected wave is the same of the wave that hits it thus...(not sure though)

    [tex] f '= (v/(v-vs))f [/tex]

    v= velocity of sound in air = 351.578m/s (35 deg celcius)
    f= 300Hz
    vs= 30m/s

    [tex] f '= [(351.578m/s)/ (351.578m/s -30m/s)]*(300Hz) = 327.9869 Hz [/tex]


    d) does the driver detect a beat frequency? Yes then find the beat frequency if no explain why not.

    I'm not even sure what that is however I tried looking online and found that a beat frequency is made up of more than one wave and also each wave has different frequencies...thus I think that since the police car siren has one frequency and the reflected wave has the same frequency I think and so my conclusion would be there is no beat frequency

    IS this right?

    (I saw an example however where a police car(stationary) had a radar wave which was directed toward a moving vehicle and the reflected waves created a beat frequency but this is the opposite in my case with the police car moving and instead of a stationary vehicle there is a wall Thus I'm really not sure now)


    Can someone help me out?

    THANKS
     
    Last edited: Feb 23, 2008
  2. jcsd
  3. Feb 24, 2008 #2

    Doc Al

    User Avatar

    Staff: Mentor

    Looks good.
    Looks good.
    I would agree with that statement. But note that the driver is moving towards that reflected wave.

    This is the frequency heard by someone standing by the warehouse. It gets reflected and then heard by the approaching car.


    The question is: Does the driver hear two different frequencies? He can certainly hear his own siren. How does the frequency of the reflected wave sound to the driver? (That's the answer to the previous part.)
     
  4. Feb 24, 2008 #3

    ~christina~

    User Avatar
    Gold Member

    so that creates 2 waves...I never thought of it like that.
    But wouldnt the frequency heard by the driver be and average of the 2 waves thus:

    [tex]f_{av}= (300Hz + 327.9869)/2= 313.99 Hz [/tex]

    I say yes... but one is stationary and thus it's as if he wasn't moving at all right? thus I'd find the beat frequency fb= |f1-f2| and

    f1= 300Hz (originally emitted by siren)
    f2= 327.9869 Hz (reflected wave)

    fb= |300Hz- 327.9869Hz|= 27.9869Hz

    Thank you Doc :smile:
     
  5. Feb 24, 2008 #4

    Doc Al

    User Avatar

    Staff: Mentor

    No. You calculated the frequency of the sound that hits the warehouse (327.98), which reflects with the same frequency. Now the warehouse is the source and the police car is the observer. Another Doppler shift!
     
  6. Feb 24, 2008 #5

    ~christina~

    User Avatar
    Gold Member

    wait..so the last part is incorrect?
    --------
    Oh...wow..

    so observer is moving toward the source...thus I think it'd be..

    f'= ((v+ v_o)/v)f

    v= 351.578m/s => speed of sound at 35 deg celcius
    [tex]v_o= 30m/s [/tex]
    f= 327.9869 Hz

    f'=((351.578m/s + 30m/s)/ 351.578 m/s)(327.9869Hz)= 355.973Hz

    Is this right now? I think that it should but the last part where they say if there is a beat frequency...do I use this f I found and subtract that from the 300Hz that the police car has initially?

    thus

    fb= |f1-f2|

    f1= 300Hz
    f2= 355.973Hz

    fb= |300Hz- 355.973Hz|= 55.973Hz

    Thanks Doc Al
     
  7. Feb 24, 2008 #6

    Doc Al

    User Avatar

    Staff: Mentor

    Looks good to me!
     
  8. Feb 24, 2008 #7

    ~christina~

    User Avatar
    Gold Member

    Yay!
    Thanks for your help :smile:
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?



Similar Discussions: Police car siren (waves)
Loading...