When a tuning fork is vibrated together with the air column of a resonance tube, 4 beats are heard per second when the temperature of the air column is 324 K or 289 K. The frequency of vibration of the air column at temperature 324 K is

Let $f_1, f_2$ be the frequencies of the air column at 324 K and 289 K respectively. 

We know, frequency of sound is $f_{sound}\propto \sqrt{T}$

$\Rightarrow \frac{f_1}{f_2}=\frac{\sqrt{T_1}}{\sqrt{T_2}}=\sqrt{\frac{324}{289}}=\frac{18}{17}$

If $f$ is the frequency of the tuning fork, 

$\Rightarrow f_1-f=4 \& f-f_2=4$

$\Rightarrow f_1-f_2=8$

$\Rightarrow \frac{18}{17}{f}_2-f_2=8$

$\Rightarrow f_2=136 Hz$

$\Rightarrow f_1=136+8=144 Hz$