A sonometer wire is vibrating is resonance with a tuning fork. Keeping the tension applied same, the length of the wire is doubled. Under what conditions would the tuning fork still be in resonance with the wire?

Explanation

To solve the problem, we need to analyze the relationship between the frequency of the sonometer wire and the length of the wire when it is vibrating in resonance with a tuning fork.

### Step-by-Step Solution:

1. **Understanding the Sonometer Wire**:
A sonometer wire is a device used to study the vibrations of strings and to measure frequency. It vibrates at certain frequencies depending on its tension, length, and mass per unit length.

2. **Frequency of the Wire**:
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