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Math Help - Help me!

  1. #1
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    Help me!

    A tuning fork with a frequency of 440 Hz is held above a resonance tube that is partially filled with water. Assuming that the speed of sound in air is 342 m/s, for what three smallest heights of the air column will resonance occur? Where will the nodes and antinodes occur? (Hint: For resonance to occur, the frequency of the tuning fork must match that of the tube.)
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  2. #2
    Grand Panjandrum
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    Quote Originally Posted by babygirl
    A tuning fork with a frequency of 440 Hz is held above a resonance tube that is partially filled with water. Assuming that the speed of sound in air is 342 m/s, for what three smallest heights of the air column will resonance occur? Where will the nodes and antinodes occur? (Hint: For resonance to occur, the frequency of the tuning fork must match that of the tube.)
    The wavelength \lambda=\frac{c}{f} in \mbox{m}, where f is the frequency in \mbox{Hz} and c is the speed of sound in \mbox{m/s}.

    For a air column closed at one end and open at the other; at resonance you
    have a node at the closed end and an anti-node at the open end, so the
    length for the lowest resonance is a quarter wavelength, the next resonance
    is three quarters of a wavelength, and the third is at one and a quarter wavelengths.

    So pluging in the numbers:

    \lambda=342/440\approx 0.777 \mbox{m},

    so the required lengths are 0.25\lambda,\ 0.75\lambda,\ 1.25\lambda.

    RonL
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