Write an equation for the position of the cart as a function of time using the given quantities above.b) Write an equation for the frequency

Question

Write an equation for the position of the cart as a function of time using the given quantities above.b) Write an equation for the frequency heard by a stationary observer standing to the right of the track as a function of time.c) If the maximum sound level heard by the person is 75 decibels when the speaker is at its closest distance 1.00 m from him, what is the minimum sound level heard by the observer in decibels

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bonexptip 3 years 2021-07-17T14:03:54+00:00 1 Answers 15 views 0

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  1. Euphemia
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    2021-07-17T14:05:04+00:00
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    Answer:

    (a). w/ 2π = 1/2π × (√k + ky/m).

    (b). Vi/( Vi + Aw sin wt) or Vi/( Vi – Aw sin wt).

    (c). 68.97 dB.

    Explanation:

    We are given that the two springs constant = k and ky respectively, mass = m.

    So, k which is the left hand spring is stretched to the right and ky which is the right hand spring is stretched to the left. Thus, we will have;

    Total force = – (k + ky) ∆x. Where ∆x = displacement.

    So, total force  = displacement.

    Thus, mw^2 ∆x =  (k + ky) ∆x.

    w^2 = (k + ky)/ m.

    Therefore, the frequency,

        = w/ 2π = 1/2π × (√k + ky/m).

    (b). In simple harmonic motion, the displacement, x(t) = A cos(wt).

    Therefore, the velocity = dx(t)/ dt = – Aw sin wt.

    Hence, the frequency heard:

    = Vi/( Vi + Aw sin wt) or Vi/( Vi – Aw sin wt).

    (C). Minimum intensity = (4π × maximum intensity)/ 4π × (2)^2.

    = Maximum intensity/ 4.

    Hence, the intensity level, y = 10 log I(min)/ I(h).

    = 10 log (0.79 × 10^7).

    = 68.97 dB.

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