Relating $\tau$ to delay of $M$ samples

For $y(n) = x(n) + x(n-M)$ delay is M samples or

$$\tau = \frac{M}{fs}$$    seconds$$.$$

There is complete attenuation (notch) at frequency

$$f = \frac{1}{2\tau} = \frac{1}{2M/f_s} = \frac{f_s}{2M}$$

and at odd harmonics $3f, 5f, ...$ (up to Nyquist limit).

For $M = 1$ (lowpass) there is 1 notch at $f_s/2$.

For $M = 6$ there are notches at $f_s/12, f_s/4, 5f_s/12$.