In certain ranges of a piano keyboard, more than one string is tuned to the same

Question

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 595 N to 551 N, what beat frequency is heard when the hammer strikes the two strings simultaneously? Part 1 of 3-Conceptualize Noticeable beat frequencies are usually only a few Hz, so we should not expect a frequency much greater than this. Part 2 of 3 - Categorize As in previous problems, the two wave speed equations can be used together to find the frequency of vibration that corresponds to a certain tension. The beat frequency is the difference between the two resulting frequencies generated by the two strings vibrating with different tensions Part 3 of 3 - Analyze Combining the velocity and the tension equations v fa and v VTlu, we find that the frequency is given by ?? Since ? and ? are constant, we can apply this equation to both frequencies, and then divide the two equations to get the proportion T1

Explanation / Answer

T2 = 551 N

f2 = (110 Hz) sqrt (551/595)

f2 = 105.85 Hz

The beat frequency,

delta f = (110 Hz) - (105.85 Hz)

delta f = 4.15 Hz

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