1. Use the formula for interference intensities

If two coherent waves have amplitudes $a_1$ and $a_2$, then:

$I_{\max}=(a_1+a_2)^2$ $I_{\min}=(a_2-a_1)^2$

So,

$\frac{I_{\max}}{I_{\min}}=\frac{(a_1+a_2)^2}{(a_2-a_1)^2}$

2. Given amplitude ratio

$\frac{a_1}{a_2}=\frac{1}{3}$

Let

$a_1=k, \quad a_2=3k$

3. Substitute into the ratio

$\frac{I_{\max}}{I_{\min}}=\frac{(k+3k)^2}{(3k-k)^2}$

$=\frac{(4k)^2}{(2k)^2}$

$=\frac{16k^2}{4k^2}=4$

4. Match with the options

Thus, the ratio of maximum to minimum intensities is:

$\boxed{4}$

So the correct option is B.