def calc_delay2(freq, freqref, dm, scale=None):
    """ Calculates the delay in seconds due to dispersion delay.
    freq is array of frequencies. delay is relative to freqref.
    default scale is 4.1488e-3 as linear prefactor (reproducing for rtpipe<=1.54 requires 4.2e-3).
    """
    scale = 0.0041488 if not scale else scale
    return scale * dm * (1.0 / freq ** 2 - 1.0 / freqref ** 2)
