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Solve the following problem using Python, implementing the functions described below, one line at a time
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Description:
 def qnm_freq_decay(f_0, tau, decay):
 """Return the frequency at which the amplitude of the ringdown falls to decay of the peak amplitude. Parameters f_0 : float The ringdown-frequency, which gives the peak amplitude. tau : float The damping time of the sinusoid. decay: float The fraction of the peak amplitude. Returns ------- f_decay: float The frequency at which the amplitude of the frequency-domain ringdown falls to decay of the peak amplitude. """


    q_0 = pi * f_0 * tau
    alpha = 1. / decay
    alpha_sq = 1. / decay / decay

    # Expression obtained analytically under the assumption
    # that 1./alpha_sq, q_0^2 >> 1
    q_sq = (alpha_sq + 4*q_0*q_0 + alpha*numpy.sqrt(alpha_sq + 16*q_0*q_0)) / 4.
    return numpy.sqrt(q_sq) / pi / tau