Given information:
- A tuning fork gives 4 beats with a 50cm length of a sonometer wire.
- If the length of the wire is shortened by 1cm, the number of beats is still the same.

Explanation:
1. Understanding beats:
- When two waves of slightly different frequencies interfere, they produce a phenomenon called beats.
- Beats are heard as a result of the constructive and destructive interference patterns between the two waves.
- The number of beats produced per second is equal to the difference in frequencies of the two waves.

2. Relationship between length and frequency:
- The length of a sonometer wire is inversely proportional to its frequency.
- As the length of the wire increases, the frequency decreases, and vice versa.

3. Initial scenario:
- The tuning fork produces 4 beats with a 50cm length of the sonometer wire.
- Let the frequency of the tuning fork be 'f' Hz.
- The frequency of the wire is equal to the frequency of the tuning fork, which is 'f' Hz.

4. Change in length:
- The length of the wire is shortened by 1cm, resulting in a new length of 49cm.
- Due to the change in length, the frequency of the wire also changes.
- Let the new frequency of the wire be 'f1' Hz.

5. Analysis of the beats:
- The number of beats produced remains the same when the length of the wire is changed.
- This implies that the difference in frequencies between the tuning fork and the wire remains the same.

6. Deriving the solution:
- Initially, the difference in frequencies between the tuning fork and the wire was 'f' Hz (let's call it Δf).
- After shortening the wire, the difference in frequencies is still 'f' Hz.
- The frequency of the wire can be represented as (f ± Δf) Hz.
- Since the difference in frequencies is positive, we can write the equation as (f - Δf) Hz = (f + Δf) Hz.
- Solving this equation, we get Δf = Δf.
- Therefore, the value of Δf remains the same before and after shortening the wire.

7. Finding the frequency of the tuning fork:
- From step 6, we know that Δf = Δf.
- Since the length of the wire and the frequency of the tuning fork are inversely proportional, the difference in frequencies is also inversely proportional to the length of the wire.
- As the length of the wire is reduced by 1cm, the difference in frequencies remains the same.
- Therefore, the frequency of the tuning fork is equal to the difference in frequencies when the length of the wire is 50cm.
- The given answer is 396 Hz.

Conclusion:
- The frequency of the tuning fork is 396 Hz.