Two tuning forks produce 4 beats per second when they are sounded together. Now both the  forks are moved towards the observer at same speed $\left(u\right).$  The beat frequency now becomes $5Hz.$  If the observer also begins to run with speed $u$ towards both the forks, what beat frequency will he hear now ?

The frequencies of two forks are assumed to be f and  $f+4.$
When forks are moving towards the observer, the frequencies received by the observer are
$f_1=f\left(\frac{v}{v-u}\right)$  and   $f_2=(f+4)\left(\frac{v}{v-u}\right)$
 $\therefore \Delta f=f_2-f_1=4\left(\frac{v}{v-u}\right)$
$\therefore 5=4\left(\frac{v}{v-u}\right) \Rightarrow 5v-5u=4v\Rightarrow u=\frac{v}{5}$
When observer also begins to run, the frequencies received by him will be 
$f_1\text{'}=f\left(\frac{v+u}{v-u}\right) and f_2\text{'}=(f+4)\left(\frac{v+u}{v-u}\right)$

$\therefore \Delta f\text{'}=f{\text{'}}_2-f{\text{'}}_1=4\left(\frac{v+u}{v-u}\right)$

$=4\left(\frac{v+\frac{v}{5}}{v-\frac{v}{5}}\right)=4\cdot \frac{6}{4}=6Hz$