3. Let $f_{1}(x)=\sqrt{2}, f_{2}(x)=\sin x+\cos \sqrt{2} x$, $f_{3}(x)=\sin \frac{x}{\sqrt{2}}+\cos \sqrt{2} x, f_{4}(x)=\sin x^{2}$. Among the above functions, the number of periodic functions is ( ).
(A) 1
(B) 2
(C) 3
(D) 4
3. B.
$f_{1}(x)=\sqrt{2}$ is a periodic function with any positive real number as its period.
Since $\sin x$ is a periodic function with period $T_{1}=2 \pi$, and $\cos \sqrt{2} x$ is a periodic function with period $T_{2}=\frac{2 \pi}{\sqrt{2}}$, and the ratio of $T_{1}$ to $T_{2}$ is not a rational number, hence $f_{2}(x)$ is not a periodic function.

Since $\sin \frac{x}{\sqrt{2}}$ is a periodic function with period $T_{1}=2 \sqrt{2} \pi$, and $\cos \sqrt{2} x$ is a periodic function with period $T_{2}=\frac{2 \pi}{\sqrt{2}}$, and $\frac{T_{1}}{T_{2}}=2$, hence $f_{3}(x)$ is a periodic function. $f_{4}(x)=\sin x^{2}$ is not a periodic function.