Wind instruments have an adjustable joint to change the tube length. Players kno

Question

Wind instruments have an adjustable joint to change the tube length. Players know that they may need to adjust this joint to stay in tune-that is, to stay at the correct frequency. To see why, suppose a "cold" flute plays the note A at 440 Hz when the air temperature is 20°C. Treat the flute as an open-open tube. 1. How long is the tube? At 20°C, the speed of sound in air is 343 m/s. 2. As the player blows air through the flute, the air inside the instrument warms up. Once the air temperature inside the flute has risen to 32°C, increasing the speed of sound to 350 m/s, what is the frequency? At the higher temperature, how must the length of the tube be changed to bring the frequency back to 440 Hz? 3.

Explanation / Answer

Given

open tube organ pipe the fundamental frequency is  

f1 = v/2L

at 20 0C

1)

so the length of the pipe is L = v/2f1 = 343/(2*440) m = 0.3898 m

2) as the temperature is increased to 32 0C then the  

speed of the sound is v = 331+0.6*T

v = 331+0.6*32 m/s

v = 350.2 m/s

so the frequency is f = v/2L = 350/(2*0.3899) Hz

f = 448.833 Hz

3) f = v/2L

440 = 350/(2*L)

L = 0.3977 m

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