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Homework Help: Doppler effect speaker problem

  1. Mar 20, 2005 #1
    A block with a speaker bolted to it is connected to a spring having spring constant k = 21.0 N/m, as in Figure P17.40. The total mass of the block and speaker is 46.00 kg, and the amplitude of this unit's motion is 0.475 m. Assume that the speed of sound is 343 m/s.

    Figure P17.40 (http://www.webassign.net/pse/p17-38.gif)

    (a) If the speaker emits sound waves of frequency 470 Hz, determine the highest and lowest frequencies heard by the person to the right of the speaker to the nearest 0.01 Hz.
    Hz (highest)
    Hz (lowest)
    (b) If the maximum sound level heard by the person is 66.0 dB when he is closest to the speaker, 1.00 m away, what is the minimum sound level heard by the observer?

    Was thinking you would have to use f'=(v -v0 / v) but that won't work. Not sure how to fit in the given values such as the spring constant and the amplitude. Please help!!
  2. jcsd
  3. Mar 21, 2005 #2
    In the doppler shift equation, you need the velocity of the source (speaker). The source under goes SHM and you need the information given such as k, m to find velocity.

    The displacement of the speaker is given by x = A sin(wt) where A is the amplidtude (given) and w = sqrt (k/m).

    Find the velocity by differentiating the above.

    V= Aw cos(wt). Listner will hear minimum frequency when the speaker moves away from him and maximum frequency when it moves towards him. Speaker's maximum speed is Aw at the equillibrium point O.

    A.............O..................B * (Listner)

    Min frequency f- = f c/ (c + v)
    Max frequency f+ = f c / (c-v)
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