A wire of length 80 cm has a frequency of 256 Hz. Calculate the length of a similar wire under similar tension, which will have frequency of 1024 Hz.

Explanation

To solve the problem, we need to use the relationship between the frequency of a wire and its length. The frequency (f) of a vibrating wire is inversely proportional to its length (L) when the tension and other properties remain constant.

### Step-by-Step Solution:

1. **Identify Given Values:**
- Length of the first wire (L1) = 80 cm
- Frequency of the first wire (f1) = 256 Hz
- Frequency of the second wire (f2) = 1024 Hz
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