Let v be the frequency of tuning fork.

Let, v_{1} and v_{2 }be the frequencies of sonometer wire when its length is 30cm and 31 cm respectively.

The frequency of sonometer wire is inversely proportional to the length of the sonometer wire.

Therefore

v1/v_{2}=31/30 ......(1)

From the above equation, it is clear that v_{1} > v_{2} . Since tuning fork produces 4 beats per second with sonometer wire for both lengths, therefore

v_{1}>v_{2}

v_{1}-v=4

=> v_{1}=v+4

and v_{1}-v_{2}=4

=> v_{2}=v-4

thus, v_{1}/v_{2}=v+4/v-4 ......(2)

from (1) and (2)

v+4/v-4=31/30

(v+4)30=31(v-4)

After solving we get

v=244 Hz , is the frequency of the tuning fork.