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Activity Based Physics Thinking Problems in Oscillations and Waves:

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    Activity Based Physics Thinking Problems in Oscillations and Waves: Sound

    1) A 15 cm violin string, fixed at both ends, is vibrating in its fundamental mode (no nodes other than the endpoints). The speed of waves in this wire is 250 m/s and the speed of sound in air is 350 m/s. What are (a) the frequency and (b) the wavelength of the emitted sound wave?

    2) You decide to build a pipe organ in your dormitory room using PVC pipe. Estimate whether you could build an organ that would cover the entire range of human hearing without bending any pipes.

    3) I have set up my two stereo speakers in my living room as shown in the top view diagram in the figure at the right. I am worried that from some positions in the room I will lose some important frequencies as a result of interference.

    The coordinate grid on the edge of the picture has its large tick marks separated by 1 meter. For ease of calculation, make the following assumptions:

      a) Assume that the relevant objects lie on integer or half-integer grid points of the coordinate system.
      b) Take the speed of sound to be 330 m/s.
      c) Ignore the reflection of sound from the walls, floor, ceiling, and objects in the room.
      d) The speakers are in phase.

    (a) If I am sitting in my favorite chair (the one on the left), what will be the lowest frequency I will lose to destructive interference? (If you do not have a calculator, leave the result as an expression with numbers that could be simply evaluated and estimate the result to one significant figure.)
    (b) What will happen if I am sitting in the middle of the sofa?
    (c) Can I restore the frequency lost in part (a) by switching the leads to one of the speakers, thereby reversing the phase of that source?
    (d) With the leads reversed, what will happen to the sound for a person sitting at the center of the sofa?

These problems written and collected by E. F. Redish. These problems may be freely used in classrooms. They may be copied and cited in published work if the Activity Based Physics Thinking Problems in Physics site is mentioned and the URL given. Web page created and edited by K. A. Vick.

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Last modified June 21, 2002