A flutist assembles her flute in a room where the speed of s

A flutist assembles her flute in a room where the speed of sound is 342 m/s . When she plays the note A, it is in perfect tune with a 440 Hz tuning fork. After a few minutes, the air inside her flute has warmed to where the speed of sound is 344 m/s .

How many beats per second will she hear if she now plays the note A as the tuning fork is sounded? How far does she need to extend the \"tuning joint\" of her flute to be in tune with the tuning fork?

Solution

f₁ = v₁ / 2 L = 440

342 / 2 L = 440

2L = 342 / 440

v₂ = 344 m/s

f₂ = v₂ / 2 L = 344 / 2L = 344 * 440 / 342

Beat frequenvy f = f₂ - f₁ = [344 * 440 / 342] - 440

= 2.57 = 3.0 beats/s

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f₂ > f₁

Length is not able to keep ratio with increased speed of sound

increase L to (L+x)

344 / 2(L+x) = 440

2L + 2x = 344 / 440

[ 342 / 440 ] + 2x = 344 / 440

2 x = 2 / 440

x = 0.00227 m = 2.27 mm