A sonometer wire with a natural frequency of 240 Hz is made to...

When a sonometer wire is made to vibrate by an external source such as a tuning fork, it undergoes forced vibrations.

In forced vibrations, the system oscillates with the frequency of the applied external periodic force, irrespective of its natural frequency.

Since the frequency of the tuning fork is $480 \text{ Hz}$, the sonometer wire will vibrate with a frequency of $480 \text{ Hz}$.

As $480 \text{ Hz}$ is an integer multiple of the natural frequency ($2 \times 240 \text{ Hz}$), the wire will vibrate in its second harmonic (resonance), but the frequency of vibration will be exactly $480 \text{ Hz}$.