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In certain ranges of a piano keyboard , ...

In certain ranges of a piano keyboard , more than one string is tuned to the same note to provide extra loudness . For example , the note at `110 Hz` has two strings at this frequency . If one string slips from its normal tension of `600 N "to" 540 N` , what beat frequency is heard when the hammer strikes the two strings simultaneously ?

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To solve the problem of finding the beat frequency when one string of a piano slips from its normal tension, we can follow these steps: ### Step-by-Step Solution: 1. **Understanding the Problem**: We have two strings tuned to the same frequency of 110 Hz. One string is under normal tension (600 N), and the other string is under reduced tension (540 N). We need to find the beat frequency when both strings are struck simultaneously. 2. **Using the Relationship Between Frequency and Tension**: The frequency of a vibrating string is related to its tension (T) and linear mass density (μ) by the formula: \[ ...
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