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Find the fundamental frequency and the f...

Find the fundamental frequency and the first four overtones of a ` 15 cm` pipe (a) if the pipe is closed at one end , and (b) if the pipe is open at both ends. ( c) How many overtones may be heard by a person of normal hearing in each of the above cases ? velocity of sound in air ` = 330 m//s`.

Text Solution

Verified by Experts

The correct Answer is:
550, 1650 , 2750, 3850, 4950 Hz
For a closed pipe, we use
`n_(0) = (v)/(4l) = (330)/(4 xx 0.15) ` = 550 Hz
As in closed pipe only odd harmonics are present, we use
`n_(1_(0)T) = 3n_(0) = 1650 Hz`
`n_(2_(0)T) = 3n_(0) = 2750 Hz`
`n_(3_(0)T) = 7n_(0) = 3850 Hz`
`n_(4_(0)T) = 9n_(0) = 4950 Hz`
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Knowledge Check

  • The fundamental frequency of an open pipe of length 34cm and how many harmonics may be heard by a person having normal hearing ?

    A
    100Hz, 10
    B
    300 Hz, 30
    C
    200 Hz, 20
    D
    500 Hz, 40

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    `100, 200, 300, 400, "….."`
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    `100, 300, 500, 700, "……"`
    C
    `200, 300, 400 , 500, "……"`
    D
    `200, 400, 600, 800, "….."`

  • The ratio of fundamental frequency of an organ pipe opened at both ends to that of the organ pipe closed at one end is :

    A
    `1:1`
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