You have two aluminum tubes which each have one end closed. While at room temperature (20◦ C) they each have a length of 10 centimeters. You decide to make a new type of thermometer in which you let one tube equalize with the outside air, while keeping the second at 20◦ C. When each tube plays their fundamental frequency you hear a beat frequency of 0.5 Hz. What are the two possible outside temperatures?
For this problem you can assume the speed of sound in air is constant at 343 m/s. The linear coefficient of thermal expansion for aluminum is 22.2 ×10^−6 K^−1.