Karplus Strong - getting a pluck of particular frequency
You are confusing normalized frequency with real frequency (Hz). Wikipedia Normalized Frequency.

The equation for the fundamental frequency (\$f_0\$) given number of delay units in the "string" (\$M\$) should be \$f_0=\frac{F_s}{M}\$, as the website states. Note that the Karplus Strong algorithm (formulated for a plucked string) is no more than a feedback comb filter initialized to a noise burst, which has frequency response: \$H(\omega)=\frac{1}{1-\alpha e^{-j \omega M }}\$, where \$\alpha\$ is the scaling factor from your original difference equation. 

Here is the magnitude plot with \$\alpha=.5\$ and \$M = 10\$:

Wolfram Alpha Plot

Note that the peaks are at \$\omega = 0, \pi/5, 2\pi/5...\$ This implies the fundamental frequency is at \$\omega_0 = \pi/5\$, which corresponds to the "real" frequency of \$44100/10 = 4410\$ Hz (assuming 44100 samples / sec). Remember that the fifth harmonic in this case is \$\omega_5 =5\pi/5 = \pi\$. This corresponds to what we expect, the fifth harmonic is 22050 Hz, the highest frequency we can represent with a sample rate of 44100 samples / sec.

Think about what happens in the frequency domain: over time, the initialized noise burse (which looks fairly uniform in frequency) gets filtered by the peaked harmonic response of the filter, which produces the harmonics you expect for a plucked string.