  Let $u_k$ be a solution of the Helmholtz equation with the wave number $k$,
$\Delta u_k+k^2 u_k=0$, on a small ball in either $\mathbb{R}^n$,
$\mathbb{S}^n$, or $\mathbb{H}^n$. For a fixed point $p$, we define
$M_{u_k}(r)=\max_{d(x,p)\le r}|u_k(x)|.$ The following three ball inequality
$M_{u_k}(2r)\le C(k,r,\alpha)M_{u_k}(r)^{\alpha}M_{u_k}(4r)^{1-\alpha}$ is well
known, it holds for some $\alpha\in (0,1)$ and $C(k,r,\alpha)>0$ independent of
$u_k$. We show that the constant $C(k,r,\alpha)$ grows exponentially in $k$
(when $r$ is fixed and small). We also compare our result with the increased
stability for solutions of the Cauchy problem for the Helmholtz equation on
Riemannian manifolds.
