A tuba may be treated like a tube closed at one end. If a tuba has a fundamental frequency of 40.4 Hz, determine the first three overtones.

Question

A tuba may be treated like a tube closed at one end. If a tuba has a fundamental frequency of 40.4 Hz, determine the first three overtones. Use 343 m/s as the speed of sound in air.
If the speed of sound is 337 m/s, determine the length of an open tube (open at both ends) that has a fundamental frequency of 233 Hz and a first overtone frequency of 466 Hz.

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Latifah 5 years 2021-09-01T13:44:29+00:00 1 Answers 12 views 0

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  1. Doris
    0
    2021-09-01T13:46:08+00:00
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    Answer:

    Explanation:

    fundamental frequency at closed pipe = 40.4 Hz

    overtones are odd harmonics in closed pipe

    first three overtones are

    3 x 40.4 , 5 x 40.4 , 7 x 40.4 Hz

    = 121.2 Hz , 202 Hz , 282.8 Hz .

    speed of sound given is 337 , fundamental frequency is 233 Hz

    wavelength = velocity of sound / frequency

    = 337 / 233

    = 1.446 m

    for fundamental note in open pipe

    wavelength /2 = length of tube

    length of tube = 1.446 / 2

    = .723 m

    = 72.30 cm .

    first overtone will be two times the fundamental ie 466. In open pipe all the harmonics are found , ie both odd and even .

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