The vibration portion of a wire which isstretched with a weight of6.48kg weighs 0.5 gm.When sounding in fundamental note, it isfound togive20 beats in5 seconds, witha vibrating tuning fork of frequency 256. If the length of the wire is slightly decreased, the note emitted by it is observed to be in unison withthat ofthe fork. Calculatethe original length of the wire.

Explanation

To solve the problem step by step, we will follow the information provided in the question and the video transcript.

### Step 1: Determine the frequency of the wire before the length is decreased.

The wire produces 20 beats in 5 seconds with a tuning fork of frequency 256 Hz.

To find the frequency of the wire (f1):
- The number of beats per second = Number of beats / Time = 20 beats / 5 seconds = 4 beats/second.
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