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6 May, 10:40

The fundamental frequency of an open organ pipe corresponds to B above middle C (493.9 Hz on the chromatic musical scale). The third resonance of a different closed organ pipe has the same frequency. What are the lengths of the two pipes? (Assume that the speed of sound in air is 343 m/s.)

1. open pipe

m

2. closed pipe

m

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Answers (1)
  1. 6 May, 14:39
    0
    For open end the length of pipe is 0.347 meter.

    The length of pipe for closed end is 0.521 meter.

    Explanation:

    Given

    fundamental frequency = f 1 = 493.9 Hz

    Velocity of sound = v = 343 m/s

    1. For open end pipe the formula for frequency = (n*v) / 2*l

    v stands for velocity

    n represent number of harmonics or resonance

    l stands for length of the pipe

    f 1 = (n*v) / (2*l)

    we want to find out the length of open end pipe so

    f 1 * 2*l = n*v

    l = (n*v) / (2*f 1)

    l = (1*343) / (2*493.9)

    l = 343/987.8

    l = 0.347 m

    For open end the length of pipe is 0.347 meter.

    Part B

    For close end pipe the formula for frequency = f = (n*v) / (4*l)

    f = (n*v) / (4*l)

    we want to find the length of closed pipe

    f * 4*l = n*v

    l = (n*v) / (4*f)

    n=3 for third resonance

    frequency will be same as fundamental frequency=f 1=f 3 = 493.9 Hz (given)

    v = 343 m/s

    l = (n*v) / (4*f)

    Now put the values in above equation

    l = (3*343) / (4*493.9)

    l = 1029/1975.6

    l = 0.521 m

    The length of pipe for closed end is 0.521 meter
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