The overall length of a piccolo is 30.0 cm. The resonating air column is open at both ends. (a) Find the frequency of the lowest note a picc

Question

The overall length of a piccolo is 30.0 cm. The resonating air column is open at both ends. (a) Find the frequency of the lowest note a piccolo can sound. (Assume that the speed of sound in air is 343 m/s.) Hz (b) Opening holes in the side of a piccolo effectively shortens the length of the resonant column. Assume the highest note a piccolo can sound is 3 000 Hz. Find the distance between adjacent antinodes for this mode of vibration.

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Kiệt Gia 19 mins 2021-07-22T14:22:35+00:00 1 Answers 0 views 0

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    2021-07-22T14:24:26+00:00

    Answer:

    (a)  the frequency of the lowest note the piccolo can sound is 571.7 Hz

    (b) the distance between adjacent antinodes is 5.72 cm

    Explanation:

    (a)

    Given;

    length of piccolo, L = 30 cm = 0.3 m

    the speed of sound in air is 343 m/s

    The wavelength of a pipe open at both ends, for the first harmonic is given;

    L = A → N + N → A

    L = λ / 4 +  λ / 4

    L = λ / 2

    λ = 2L

    λ = 2 x 0.3 = 0.6 m

    The fundamental frequency (lowest frequency) is given  by;

    f₀ = v / λ

    f₀ = (343 / 0.6)

    f₀ = 571.7 Hz

    (b)

    Given;

    highest note, f = 3000 Hz

    the distance between adjacent antinodes is given by;

    d = \frac{v}{2f}\\\\ d = \frac{343}{2*3000}\\\\ d = 0.0572 \ m\\\\d = 5.72 \ cm

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