Two loudspeakers, 4.5 m apart and facing each other, play identical sounds of the same frequency. You stand halfway between them, where ther

Question

Two loudspeakers, 4.5 m apart and facing each other, play identical sounds of the same frequency. You stand halfway between them, where there is a maximum of sound intensity. Moving from this point toward one of the speakers, you encounter a minimum of sound intensity when you have moved 0.21 m . Assume the speed of sound is 340 m/s.

Part A

What is the frequency of the sound?

Part B

If the frequency is then increased while you remain 0.35m from the center, what is the first frequency for which that location will be a maximum of sound intensity?

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Euphemia 6 months 2021-07-15T03:45:12+00:00 1 Answers 3 views 0

Answers ( )

    0
    2021-07-15T03:46:47+00:00

    Answer:

    Explanation:

    Given that,

    Distance between speaker

    L = 4.5m

    Minimum intensity at L1 = 0.21m

    Speed of sound is

    V = 340m/s

    A. Frequency of sound f?

    The path difference Pd

    Distance from the first speaker when you are 0.21m away

    d1 = 2.25 + 0.21 = 2.46m

    Distance from the second speaker when you move 0.21m closer

    d2 = 2.25—0.21 = 2.04m

    So, path difference is

    Pd = ∆d = d1 — d2

    Pd = 2.46—2.04 = 0.42m

    Using the destructive interference condition

    ∆d = (m + ½)λ

    m = 0,1,2,3….

    When m= 0

    ∆d = ½λ

    0.42 = ½λ

    λ = 0.84

    Then, using wave equation

    v = fλ

    Then, f = v / λ

    f = 340 / 0.84

    f = 404.76Hz

    B. Incorrect question

    If he is to remain at his initial positions then it is 0.21m from the center.

    Then,

    Constructive interference is given as

    ∆d = mλ

    Where m = 0,1,2,3

    So when m= 1

    ∆d = λ

    And we already got the path difference to be 0.42m

    So, ∆d = λ

    λ = 0.42

    So, applying wave equation

    V = fλ

    F = v/λ

    F = 340/0.42

    F = 809.52 Hz

    But if we are to use the data given in part B

    0.35m from the center..

    Following the same principle as part A, the path difference will be 0.35

    Therefore, since ∆d = λ

    Then, λ = 0.35

    So, f, = v/λ

    F = 340 /0.35

    F = 971.43 Hz

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