Question

A guitar string has a linear mass density of 0.005 kg/m, a tension of 100 N, and is supposed to have a fundamental frequency of 110 Hz. When a tuning fork of that frequency is sounded while the string is plucked, a beat frequency of 2 Hz is heard. The peg holding the string is tightened, increasing the tension, and the beat frequency increases.

1. Before it was tightened and while it still had a tension of 100 N, The frequency of the guitar string was ["114", "112", "106", "110", "108"]         Hz.
2. The length of the guitar string is most nearly ["78", "93", "63", "33", "48"] cm
3. To achieve the correct pitch of 110 Hz, the tension should be adjusted to ["92.7", "110", "104", "108", "96.5"]      

Answer 1

1) since on increasing the tension, the frequency of a sound produced is increased, and it is mentioned that the beat frequency is also increasing with the increasing tension the beat frequency is also increasing. It means that the original sound's frequency is greater than 110 Hz

Therefore, frequency of the sound produced is 110+2 = 112 Hz.

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