23 Nov 2019

The note that is three octaves above middle C is supposed to haveafundamental frequency of 2093 Hz. On a certain piano the steelwirethat produces this note has a cross-sectional area of 6.94x10-7 m2. The wire is stretched betweentwopegs. When the piano is tuned properly to produce thecorrectfrequency at 25.0 oC, the wire is under atensionof 847.5 N. Suppose the temperature drops to20.0oC. In addition, as an approximation, assumethat thewire is kept from contracting as the temperaturedrops.Consequenctly, the tension in the wire changes. What beatfrequencyis produced when this piano and another instrument(properly tuned)sound the note simultaneously? Steel's coefficientof linearexpansion is 12 x10-6(Co)-1 and itsYoung's modulus is 2 x1011 N/m2.

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