Calculate the effect of wave number $N$ on the spring rate $k$ for a single-turn wave spring.

The spring rate $k$ for a wave spring is proportional to the cube of the number of waves $N$. From the formula $P/f = k = \frac{E b t^3 N^4 K}{D_m^3}$, we see that doubling the number of waves from $N=3$ to $N=6$ increases the stiffness by a factor of 16 ($2^4$), assuming all other parameters are constant. This extreme sensitivity allows designers to fine-tune loads in very small increments. However, increasing $N$ reduces the maximum possible deflection $f$ before the waves interfere with each other, necessitating a balance between load capacity and stroke.