Given:

Velocity of sound $\left(v_s\right)$$=$ $4 {\mathrm{ms}}^{-1}$

Velocity of observer $\left(v_o\right)= 0 {\mathrm{ms}}^{-1}$

Frequency $\left(f_o\right)$$=$ $240$ $\mathrm{Hz}$

For first train,

From Doppler effect in sound waves,

$\Rightarrow f=f_o\left(\frac{v-v_o}{v+v_s}\right)$

  $$\begin{gathered} f_1=240\times \frac{320}{320+4} \\ =240\times \frac{320}{324} \\ {f}_1=237 Hz \end{gathered}$$

In second train coming towards observer,

$$\begin{gathered} f_2=\frac{320}{320-4}\times 240 \\ =\frac{320}{316}\times 240 \\ {f}_2 =243 Hz \end{gathered}$$

Therefore,

$$$$\begin{gathered} f= f_2-f_1 \\ f= \left(243-237\right) \\ f= 6 Hz \end{gathered}$$

A beat-frequency $f= 6 Hz$