A fluitist assembles her flute in a room which is at 15 C (DEGREES CELSIUS). Whe

Question

A fluitist assembles her flute in a room which is at 15 C (DEGREES CELSIUS). When she first plays the note E, it is in perfect tune with a 659Hz tuning fork. After a few minutes, the air inside her flute has warmed up to temperature of 24C (degrees Celsius) a. How many beats per second will she now hear if she plays the note E as the tuning fork is sounded? b. How far does she need to extend the "tuning joint" of her flute to be in tune with the tuning fork?

Explanation / Answer

At 15°C is ?20 = 1.225 kg/m3, Z20 = 417 N·s/m3, and c20 = 340 m/s At 24°C is ?20 = 1.184 kg/m3, Z25 = 410 N·s/m3, and c25 = 345 m/s a.) v = 340 m/s , f = 695 Hz = v/L => L = 0.4892 m , L is wavelength v = 345 m/s , f' = 345/L = 705 Hz(approx), Thus Beat = f' - f = 705 - 695 = 10 b.) for the same frequency i.e 695 Hz , & v = 345 m/s , L' = 345/695 = 0.4964 m Thus distance to be moved = 0.4964 - 0.4892 = 0.0072 m = 0.72 cm

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