Wind instruments have an adjustable joint to change the tube length. Players know that they may need to adjust this join 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 ℃. a. How long is the tube? At 20 ℃, the speed of sound in air is 343 m/s. b. 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 ℃, increasing the speed of sound to 350 m/s, what is the frequency? c. At the higher temperature, how must the length of the tube be changed to bring the frequency back to 440 Hz?